%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PLA002-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:22:49 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.57s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : PLA002-2 : TPTP v9.0.0. Released v1.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 02:19:23 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.57 % SZS status Unsatisfiable
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 tff(situation_type, type, (
% 0.19/0.57 situation: $i > $o)).
% 0.19/0.57 tff(walk_type, type, (
% 0.19/0.57 walk: ( $i * $i ) > $i)).
% 0.19/0.57 tff(climb_type, type, (
% 0.19/0.57 climb: ( $i * $i ) > $i)).
% 0.19/0.57 tff(go_type, type, (
% 0.19/0.57 go: ( $i * $i ) > $i)).
% 0.19/0.57 tff(s0_type, type, (
% 0.19/0.57 s0: $i)).
% 0.19/0.57 tff(d_type, type, (
% 0.19/0.57 d: $i)).
% 0.19/0.57 tff(b_type, type, (
% 0.19/0.57 b: $i)).
% 0.19/0.57 tff(a_type, type, (
% 0.19/0.57 a: $i)).
% 0.19/0.57 tff(at_type, type, (
% 0.19/0.57 at: ( $i * $i ) > $o)).
% 0.19/0.57 tff(warm_type, type, (
% 0.19/0.57 warm: $i > $o)).
% 0.19/0.57 tff(cold_type, type, (
% 0.19/0.57 cold: $i > $o)).
% 0.19/0.57 tff(f_type, type, (
% 0.19/0.57 f: $i)).
% 0.19/0.57 tff(c_type, type, (
% 0.19/0.57 c: $i)).
% 0.19/0.57 tff(skate_type, type, (
% 0.19/0.57 skate: ( $i * $i ) > $i)).
% 0.19/0.57 tff(1,plain,
% 0.19/0.57 (^[Somewhere: $i, Situation: $i] : refl(((~situation(Situation)) | situation(go(Somewhere, Situation))) <=> ((~situation(Situation)) | situation(go(Somewhere, Situation))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(2,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.57 tff(3,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(4,axiom,(![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','go_situation')).
% 0.19/0.57 tff(5,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.19/0.57 tff(6,plain,(
% 0.19/0.57 ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[5])).
% 0.19/0.57 tff(7,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.19/0.57 tff(8,plain,
% 0.19/0.57 (situation(s0) <=> situation(s0)),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(9,axiom,(situation(s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','initial_situation')).
% 0.19/0.57 tff(10,plain,
% 0.19/0.57 (situation(s0)),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.19/0.57 tff(11,plain,
% 0.19/0.57 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(s0)) | situation(go(d, s0)))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(s0)) | situation(go(d, s0)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(12,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(s0)) | situation(go(d, s0)))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(13,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(s0)) | situation(go(d, s0))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.19/0.57 tff(14,plain,
% 0.19/0.57 (situation(go(d, s0))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[13, 10, 7])).
% 0.19/0.57 tff(15,plain,
% 0.19/0.57 (^[Somewhere: $i, Situation: $i] : refl(((~situation(Situation)) | situation(climb(Somewhere, Situation))) <=> ((~situation(Situation)) | situation(climb(Somewhere, Situation))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(16,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.57 tff(17,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(18,axiom,(![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','climb_situation')).
% 0.19/0.57 tff(19,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.19/0.57 tff(20,plain,(
% 0.19/0.57 ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[19])).
% 0.19/0.57 tff(21,plain,
% 0.19/0.57 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.19/0.57 tff(22,plain,
% 0.19/0.57 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))) | ((~situation(go(d, s0))) | situation(climb(b, go(d, s0))))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))) | (~situation(go(d, s0))) | situation(climb(b, go(d, s0))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(23,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))) | ((~situation(go(d, s0))) | situation(climb(b, go(d, s0))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(24,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(climb(Somewhere, Situation)))) | (~situation(go(d, s0))) | situation(climb(b, go(d, s0)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.19/0.57 tff(25,plain,
% 0.19/0.57 (situation(climb(b, go(d, s0)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[24, 21, 14])).
% 0.19/0.57 tff(26,plain,
% 0.19/0.57 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(go(d, s0))) | situation(go(f, go(d, s0))))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(go(d, s0))) | situation(go(f, go(d, s0))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(27,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(go(d, s0))) | situation(go(f, go(d, s0))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(28,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(go(d, s0))) | situation(go(f, go(d, s0)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.19/0.57 tff(29,plain,
% 0.19/0.57 (situation(go(f, go(d, s0)))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[28, 7, 14])).
% 0.19/0.57 tff(30,plain,
% 0.19/0.57 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(go(f, go(d, s0)))) | situation(go(d, go(f, go(d, s0)))))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(go(f, go(d, s0)))) | situation(go(d, go(f, go(d, s0)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(31,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(go(f, go(d, s0)))) | situation(go(d, go(f, go(d, s0)))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(32,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(go(f, go(d, s0)))) | situation(go(d, go(f, go(d, s0))))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.19/0.57 tff(33,plain,
% 0.19/0.57 (situation(go(d, go(f, go(d, s0))))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[32, 7, 29])).
% 0.19/0.57 tff(34,plain,
% 0.19/0.57 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(go(d, go(f, go(d, s0))))) | situation(go(c, go(d, go(f, go(d, s0))))))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(go(d, go(f, go(d, s0))))) | situation(go(c, go(d, go(f, go(d, s0))))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(35,plain,
% 0.19/0.57 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | ((~situation(go(d, go(f, go(d, s0))))) | situation(go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(36,plain,
% 0.41/0.58 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(go(Somewhere, Situation)))) | (~situation(go(d, go(f, go(d, s0))))) | situation(go(c, go(d, go(f, go(d, s0)))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.41/0.58 tff(37,plain,
% 0.41/0.58 (situation(go(c, go(d, go(f, go(d, s0)))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[36, 7, 33])).
% 0.41/0.58 tff(38,plain,
% 0.41/0.58 (^[Somewhere: $i, Situation: $i] : refl(((~situation(Situation)) | situation(skate(Somewhere, Situation))) <=> ((~situation(Situation)) | situation(skate(Somewhere, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(39,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[38])).
% 0.41/0.58 tff(40,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(41,axiom,(![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','skate_situation')).
% 0.41/0.58 tff(42,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.41/0.58 tff(43,plain,(
% 0.41/0.58 ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[42])).
% 0.41/0.58 tff(44,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.41/0.58 tff(45,plain,
% 0.41/0.58 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | situation(skate(b, go(c, go(d, go(f, go(d, s0)))))))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | situation(skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(46,plain,
% 0.41/0.58 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | situation(skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(47,plain,
% 0.41/0.58 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(skate(Somewhere, Situation)))) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | situation(skate(b, go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.41/0.58 tff(48,plain,
% 0.41/0.58 (situation(skate(b, go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[47, 44, 37])).
% 0.41/0.58 tff(49,assumption,(at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))), introduced(assumption)).
% 0.41/0.58 tff(50,plain,
% 0.41/0.58 (^[Situation: $i] : refl(((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation))) <=> ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(51,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[50])).
% 0.41/0.58 tff(52,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(53,plain,
% 0.41/0.58 (^[Situation: $i] : rewrite((((~at(b, Situation)) | at(a, walk(a, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(54,plain,
% 0.41/0.58 (![Situation: $i] : (((~at(b, Situation)) | at(a, walk(a, Situation))) | (~situation(Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[53])).
% 0.41/0.58 tff(55,axiom,(![Situation: $i] : (((~at(b, Situation)) | at(a, walk(a, Situation))) | (~situation(Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','walk_b_to_a')).
% 0.41/0.58 tff(56,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.41/0.58 tff(57,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.41/0.58 tff(58,plain,(
% 0.41/0.58 ![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[57])).
% 0.41/0.58 tff(59,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[58, 51])).
% 0.41/0.58 tff(60,plain,
% 0.41/0.58 (((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | (~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(61,plain,
% 0.41/0.58 (((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))))) <=> ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(62,plain,
% 0.41/0.58 (((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))))),
% 0.41/0.58 inference(monotonicity,[status(thm)],[61])).
% 0.41/0.58 tff(63,plain,
% 0.41/0.58 (((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | (~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.58 inference(transitivity,[status(thm)],[62, 60])).
% 0.41/0.58 tff(64,plain,
% 0.41/0.58 ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(65,plain,
% 0.41/0.58 ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | (~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | (~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[64, 63])).
% 0.41/0.58 tff(66,plain,
% 0.41/0.58 ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[65, 59, 49])).
% 0.41/0.58 tff(67,plain,
% 0.41/0.58 (at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[66, 48])).
% 0.41/0.58 tff(68,plain,
% 0.41/0.58 (^[S: $i] : refl(((~situation(S)) | (~at(a, S))) <=> ((~situation(S)) | (~at(a, S))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(69,plain,
% 0.41/0.58 (![S: $i] : ((~situation(S)) | (~at(a, S))) <=> ![S: $i] : ((~situation(S)) | (~at(a, S)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[68])).
% 0.41/0.58 tff(70,plain,
% 0.41/0.58 (![S: $i] : ((~situation(S)) | (~at(a, S))) <=> ![S: $i] : ((~situation(S)) | (~at(a, S)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(71,plain,
% 0.41/0.58 (^[S: $i] : rewrite(((~at(a, S)) | (~situation(S))) <=> ((~situation(S)) | (~at(a, S))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(72,plain,
% 0.41/0.58 (![S: $i] : ((~at(a, S)) | (~situation(S))) <=> ![S: $i] : ((~situation(S)) | (~at(a, S)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[71])).
% 0.41/0.58 tff(73,axiom,(![S: $i] : ((~at(a, S)) | (~situation(S)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','prove_you_can_get_to_a_in_a_situation')).
% 0.41/0.58 tff(74,plain,
% 0.41/0.58 (![S: $i] : ((~situation(S)) | (~at(a, S)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.41/0.58 tff(75,plain,
% 0.41/0.58 (![S: $i] : ((~situation(S)) | (~at(a, S)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.41/0.58 tff(76,plain,(
% 0.41/0.58 ![S: $i] : ((~situation(S)) | (~at(a, S)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[75])).
% 0.41/0.58 tff(77,plain,
% 0.41/0.58 (![S: $i] : ((~situation(S)) | (~at(a, S)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.41/0.58 tff(78,plain,
% 0.41/0.58 (((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | ((~situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))) | (~at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))))) <=> ((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | (~situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))) | (~at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(79,plain,
% 0.41/0.58 ((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | ((~situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))) | (~at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(80,plain,
% 0.41/0.58 ((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | (~situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))) | (~at(a, walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.41/0.58 tff(81,plain,
% 0.41/0.58 (~situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[80, 77, 67])).
% 0.41/0.58 tff(82,plain,
% 0.41/0.58 (^[Somewhere: $i, Situation: $i] : refl(((~situation(Situation)) | situation(walk(Somewhere, Situation))) <=> ((~situation(Situation)) | situation(walk(Somewhere, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(83,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[82])).
% 0.41/0.58 tff(84,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation))) <=> ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(85,axiom,(![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','walk_situation')).
% 0.41/0.58 tff(86,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.41/0.58 tff(87,plain,(
% 0.41/0.58 ![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[86])).
% 0.41/0.58 tff(88,plain,
% 0.41/0.58 (![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[87, 83])).
% 0.41/0.58 tff(89,plain,
% 0.41/0.58 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | (~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(90,plain,
% 0.41/0.58 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | ((~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(91,plain,
% 0.41/0.58 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | (~situation(skate(b, go(c, go(d, go(f, go(d, s0))))))) | situation(walk(a, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.41/0.58 tff(92,plain,
% 0.41/0.58 ($false),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[91, 88, 48, 81])).
% 0.41/0.58 tff(93,plain,(~at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))), inference(lemma,lemma(discharge,[]))).
% 0.41/0.58 tff(94,plain,
% 0.41/0.58 (at(f, s0) <=> at(f, s0)),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(95,axiom,(at(f, s0)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','initial')).
% 0.41/0.58 tff(96,plain,
% 0.41/0.58 (at(f, s0)),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.41/0.58 tff(97,plain,
% 0.41/0.58 (^[Situation: $i] : refl(((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation))) <=> ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(98,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[97])).
% 0.41/0.58 tff(99,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(100,plain,
% 0.41/0.58 (^[Situation: $i] : rewrite((((~at(f, Situation)) | at(d, go(d, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(101,plain,
% 0.41/0.58 (![Situation: $i] : (((~at(f, Situation)) | at(d, go(d, Situation))) | (~situation(Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[100])).
% 0.41/0.58 tff(102,axiom,(![Situation: $i] : (((~at(f, Situation)) | at(d, go(d, Situation))) | (~situation(Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','go_f_to_d')).
% 0.41/0.58 tff(103,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.41/0.58 tff(104,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[103, 99])).
% 0.41/0.58 tff(105,plain,(
% 0.41/0.58 ![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[104])).
% 0.41/0.58 tff(106,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[105, 98])).
% 0.41/0.58 tff(107,plain,
% 0.41/0.58 (((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | ((~situation(s0)) | at(d, go(d, s0)) | (~at(f, s0)))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | (~situation(s0)) | at(d, go(d, s0)) | (~at(f, s0)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(108,plain,
% 0.41/0.58 ((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | ((~situation(s0)) | at(d, go(d, s0)) | (~at(f, s0)))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(109,plain,
% 0.41/0.58 ((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | (~situation(s0)) | at(d, go(d, s0)) | (~at(f, s0))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.41/0.58 tff(110,plain,
% 0.41/0.58 (at(d, go(d, s0))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[109, 106, 10, 96])).
% 0.41/0.58 tff(111,plain,
% 0.41/0.58 (^[Situation: $i] : refl(((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation))) <=> ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(112,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[111])).
% 0.41/0.58 tff(113,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(114,plain,
% 0.41/0.58 (^[Situation: $i] : rewrite((((~at(d, Situation)) | at(f, go(f, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(115,plain,
% 0.41/0.58 (![Situation: $i] : (((~at(d, Situation)) | at(f, go(f, Situation))) | (~situation(Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[114])).
% 0.41/0.58 tff(116,axiom,(![Situation: $i] : (((~at(d, Situation)) | at(f, go(f, Situation))) | (~situation(Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','go_d_to_f')).
% 0.41/0.58 tff(117,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.41/0.58 tff(118,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.41/0.58 tff(119,plain,(
% 0.41/0.58 ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.41/0.58 inference(skolemize,[status(sab)],[118])).
% 0.41/0.58 tff(120,plain,
% 0.41/0.58 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.41/0.58 tff(121,plain,
% 0.41/0.58 (((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))) | ((~situation(go(d, s0))) | (~at(d, go(d, s0))) | at(f, go(f, go(d, s0))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))) | (~situation(go(d, s0))) | (~at(d, go(d, s0))) | at(f, go(f, go(d, s0))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(122,plain,
% 0.41/0.58 ((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))) | ((~situation(go(d, s0))) | (~at(d, go(d, s0))) | at(f, go(f, go(d, s0))))),
% 0.41/0.58 inference(quant_inst,[status(thm)],[])).
% 0.41/0.58 tff(123,plain,
% 0.41/0.58 ((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(f, go(f, Situation)))) | (~situation(go(d, s0))) | (~at(d, go(d, s0))) | at(f, go(f, go(d, s0)))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.41/0.58 tff(124,plain,
% 0.41/0.58 ((~situation(go(d, s0))) | at(f, go(f, go(d, s0)))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[123, 120, 110])).
% 0.41/0.58 tff(125,plain,
% 0.41/0.58 (at(f, go(f, go(d, s0)))),
% 0.41/0.58 inference(unit_resolution,[status(thm)],[124, 14])).
% 0.41/0.59 tff(126,plain,
% 0.41/0.59 (((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | ((~situation(go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0)))) | (~at(f, go(f, go(d, s0)))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | (~situation(go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0)))) | (~at(f, go(f, go(d, s0)))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(127,plain,
% 0.41/0.59 ((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | ((~situation(go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0)))) | (~at(f, go(f, go(d, s0)))))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(128,plain,
% 0.41/0.59 ((~![Situation: $i] : ((~situation(Situation)) | at(d, go(d, Situation)) | (~at(f, Situation)))) | (~situation(go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0)))) | (~at(f, go(f, go(d, s0))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.41/0.59 tff(129,plain,
% 0.41/0.59 ((~situation(go(f, go(d, s0)))) | at(d, go(d, go(f, go(d, s0))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[128, 106, 125])).
% 0.41/0.59 tff(130,plain,
% 0.41/0.59 (at(d, go(d, go(f, go(d, s0))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[129, 29])).
% 0.41/0.59 tff(131,plain,
% 0.41/0.59 (^[Situation: $i] : refl(((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation))) <=> ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(132,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[131])).
% 0.41/0.59 tff(133,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(134,plain,
% 0.41/0.59 (^[Situation: $i] : rewrite((((~at(d, Situation)) | at(c, go(c, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(135,plain,
% 0.41/0.59 (![Situation: $i] : (((~at(d, Situation)) | at(c, go(c, Situation))) | (~situation(Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[134])).
% 0.41/0.59 tff(136,axiom,(![Situation: $i] : (((~at(d, Situation)) | at(c, go(c, Situation))) | (~situation(Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','go_d_to_c')).
% 0.41/0.59 tff(137,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.41/0.59 tff(138,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.41/0.59 tff(139,plain,(
% 0.41/0.59 ![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[138])).
% 0.41/0.59 tff(140,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.41/0.59 tff(141,plain,
% 0.41/0.59 (((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))) | ((~situation(go(d, go(f, go(d, s0))))) | (~at(d, go(d, go(f, go(d, s0))))) | at(c, go(c, go(d, go(f, go(d, s0))))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))) | (~situation(go(d, go(f, go(d, s0))))) | (~at(d, go(d, go(f, go(d, s0))))) | at(c, go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(142,plain,
% 0.41/0.59 ((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))) | ((~situation(go(d, go(f, go(d, s0))))) | (~at(d, go(d, go(f, go(d, s0))))) | at(c, go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(143,plain,
% 0.41/0.59 ((~![Situation: $i] : ((~situation(Situation)) | (~at(d, Situation)) | at(c, go(c, Situation)))) | (~situation(go(d, go(f, go(d, s0))))) | (~at(d, go(d, go(f, go(d, s0))))) | at(c, go(c, go(d, go(f, go(d, s0)))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.41/0.59 tff(144,plain,
% 0.41/0.59 ((~situation(go(d, go(f, go(d, s0))))) | at(c, go(c, go(d, go(f, go(d, s0)))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[143, 140, 130])).
% 0.41/0.59 tff(145,plain,
% 0.41/0.59 (at(c, go(c, go(d, go(f, go(d, s0)))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[144, 33])).
% 0.41/0.59 tff(146,plain,
% 0.41/0.59 (^[Situation: $i] : refl(((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) <=> ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(147,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[146])).
% 0.41/0.59 tff(148,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(149,plain,
% 0.41/0.59 (^[Situation: $i] : trans(monotonicity(rewrite((((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation))) <=> ((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))), (((((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation))) | (~situation(Situation))) <=> (((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) | (~situation(Situation))))), rewrite((((~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))), (((((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(150,plain,
% 0.41/0.59 (![Situation: $i] : ((((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation))) | (~situation(Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[149])).
% 0.41/0.59 tff(151,axiom,(![Situation: $i] : ((((~cold(Situation)) | (~at(c, Situation))) | at(b, skate(b, Situation))) | (~situation(Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cross_river_c_to_b')).
% 0.41/0.59 tff(152,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.41/0.59 tff(153,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[152, 148])).
% 0.41/0.59 tff(154,plain,(
% 0.41/0.59 ![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.41/0.59 inference(skolemize,[status(sab)],[153])).
% 0.41/0.59 tff(155,plain,
% 0.41/0.59 (![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[154, 147])).
% 0.41/0.59 tff(156,plain,
% 0.41/0.59 (((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(157,plain,
% 0.41/0.59 (((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0))))))) <=> ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(158,plain,
% 0.41/0.59 (((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[157])).
% 0.41/0.59 tff(159,plain,
% 0.41/0.59 (((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.59 inference(transitivity,[status(thm)],[158, 156])).
% 0.41/0.59 tff(160,plain,
% 0.41/0.59 ((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))))),
% 0.41/0.59 inference(quant_inst,[status(thm)],[])).
% 0.41/0.59 tff(161,plain,
% 0.41/0.59 ((~![Situation: $i] : ((~situation(Situation)) | (~cold(Situation)) | at(b, skate(b, Situation)) | (~at(c, Situation)))) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | (~at(c, go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.59 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.41/0.59 tff(162,plain,
% 0.41/0.59 ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[161, 155, 145])).
% 0.41/0.59 tff(163,plain,
% 0.41/0.59 ((~cold(go(c, go(d, go(f, go(d, s0)))))) | at(b, skate(b, go(c, go(d, go(f, go(d, s0))))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[162, 37])).
% 0.41/0.59 tff(164,plain,
% 0.41/0.59 (~cold(go(c, go(d, go(f, go(d, s0)))))),
% 0.41/0.59 inference(unit_resolution,[status(thm)],[163, 93])).
% 0.41/0.59 tff(165,plain,
% 0.41/0.59 (^[Situation1: $i, Situation2: $i] : refl(((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1)) <=> ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1)))),
% 0.41/0.59 inference(bind,[status(th)],[])).
% 0.41/0.59 tff(166,plain,
% 0.41/0.59 (![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1)) <=> ![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))),
% 0.41/0.59 inference(quant_intro,[status(thm)],[165])).
% 0.41/0.59 tff(167,plain,
% 0.41/0.59 (![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1)) <=> ![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(168,plain,
% 0.43/0.59 (^[Situation1: $i, Situation2: $i] : trans(monotonicity(trans(monotonicity(rewrite((warm(Situation1) | cold(Situation2)) <=> (cold(Situation2) | warm(Situation1))), (((warm(Situation1) | cold(Situation2)) | (~situation(Situation1))) <=> ((cold(Situation2) | warm(Situation1)) | (~situation(Situation1))))), rewrite(((cold(Situation2) | warm(Situation1)) | (~situation(Situation1))) <=> ((~situation(Situation1)) | cold(Situation2) | warm(Situation1))), (((warm(Situation1) | cold(Situation2)) | (~situation(Situation1))) <=> ((~situation(Situation1)) | cold(Situation2) | warm(Situation1)))), ((((warm(Situation1) | cold(Situation2)) | (~situation(Situation1))) | (~situation(Situation2))) <=> (((~situation(Situation1)) | cold(Situation2) | warm(Situation1)) | (~situation(Situation2))))), rewrite((((~situation(Situation1)) | cold(Situation2) | warm(Situation1)) | (~situation(Situation2))) <=> ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))), ((((warm(Situation1) | cold(Situation2)) | (~situation(Situation1))) | (~situation(Situation2))) <=> ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))))),
% 0.43/0.59 inference(bind,[status(th)],[])).
% 0.43/0.59 tff(169,plain,
% 0.43/0.59 (![Situation1: $i, Situation2: $i] : (((warm(Situation1) | cold(Situation2)) | (~situation(Situation1))) | (~situation(Situation2))) <=> ![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))),
% 0.43/0.59 inference(quant_intro,[status(thm)],[168])).
% 0.43/0.59 tff(170,axiom,(![Situation1: $i, Situation2: $i] : (((warm(Situation1) | cold(Situation2)) | (~situation(Situation1))) | (~situation(Situation2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','warm_or_cold')).
% 0.43/0.59 tff(171,plain,
% 0.43/0.59 (![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.43/0.59 tff(172,plain,
% 0.43/0.59 (![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[171, 167])).
% 0.43/0.59 tff(173,plain,(
% 0.43/0.59 ![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))),
% 0.43/0.59 inference(skolemize,[status(sab)],[172])).
% 0.43/0.59 tff(174,plain,
% 0.43/0.59 (![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))),
% 0.43/0.59 inference(modus_ponens,[status(thm)],[173, 166])).
% 0.43/0.59 tff(175,plain,
% 0.43/0.59 (((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | ((~situation(go(d, s0))) | warm(go(d, s0)) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | cold(go(c, go(d, go(f, go(d, s0))))))) <=> ((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | (~situation(go(d, s0))) | warm(go(d, s0)) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | cold(go(c, go(d, go(f, go(d, s0))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(176,plain,
% 0.43/0.59 (((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~situation(go(d, s0))) | cold(go(c, go(d, go(f, go(d, s0))))) | warm(go(d, s0))) <=> ((~situation(go(d, s0))) | warm(go(d, s0)) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | cold(go(c, go(d, go(f, go(d, s0))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(177,plain,
% 0.43/0.59 (((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~situation(go(d, s0))) | cold(go(c, go(d, go(f, go(d, s0))))) | warm(go(d, s0)))) <=> ((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | ((~situation(go(d, s0))) | warm(go(d, s0)) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | cold(go(c, go(d, go(f, go(d, s0)))))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[176])).
% 0.43/0.60 tff(178,plain,
% 0.43/0.60 (((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~situation(go(d, s0))) | cold(go(c, go(d, go(f, go(d, s0))))) | warm(go(d, s0)))) <=> ((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | (~situation(go(d, s0))) | warm(go(d, s0)) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | cold(go(c, go(d, go(f, go(d, s0))))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[177, 175])).
% 0.43/0.60 tff(179,plain,
% 0.43/0.60 ((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | ((~situation(go(c, go(d, go(f, go(d, s0)))))) | (~situation(go(d, s0))) | cold(go(c, go(d, go(f, go(d, s0))))) | warm(go(d, s0)))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(180,plain,
% 0.43/0.60 ((~![Situation1: $i, Situation2: $i] : ((~situation(Situation2)) | (~situation(Situation1)) | cold(Situation2) | warm(Situation1))) | (~situation(go(d, s0))) | warm(go(d, s0)) | (~situation(go(c, go(d, go(f, go(d, s0)))))) | cold(go(c, go(d, go(f, go(d, s0)))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.43/0.60 tff(181,plain,
% 0.43/0.60 (warm(go(d, s0)) | cold(go(c, go(d, go(f, go(d, s0)))))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[180, 174, 14, 37])).
% 0.43/0.60 tff(182,plain,
% 0.43/0.60 (warm(go(d, s0))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[181, 164])).
% 0.43/0.60 tff(183,plain,
% 0.43/0.60 (^[Situation: $i] : refl(((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) <=> ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(184,plain,
% 0.43/0.60 (![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[183])).
% 0.43/0.60 tff(185,plain,
% 0.43/0.60 (![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(186,plain,
% 0.43/0.60 (^[Situation: $i] : trans(monotonicity(rewrite((((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation))) <=> ((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))), (((((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation))) | (~situation(Situation))) <=> (((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) | (~situation(Situation))))), rewrite((((~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))), (((((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation))) | (~situation(Situation))) <=> ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))))),
% 0.43/0.60 inference(bind,[status(th)],[])).
% 0.43/0.60 tff(187,plain,
% 0.43/0.60 (![Situation: $i] : ((((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation))) | (~situation(Situation))) <=> ![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.43/0.60 inference(quant_intro,[status(thm)],[186])).
% 0.43/0.60 tff(188,axiom,(![Situation: $i] : ((((~warm(Situation)) | (~at(d, Situation))) | at(b, climb(b, Situation))) | (~situation(Situation)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','climb_mountain_d_to_b')).
% 0.43/0.60 tff(189,plain,
% 0.43/0.60 (![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[188, 187])).
% 0.43/0.60 tff(190,plain,
% 0.43/0.60 (![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[189, 185])).
% 0.43/0.60 tff(191,plain,(
% 0.43/0.60 ![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.43/0.60 inference(skolemize,[status(sab)],[190])).
% 0.43/0.60 tff(192,plain,
% 0.43/0.60 (![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[191, 184])).
% 0.43/0.60 tff(193,plain,
% 0.43/0.60 (((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~situation(go(d, s0))) | (~at(d, go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | (~situation(go(d, s0))) | (~at(d, go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(194,plain,
% 0.43/0.60 (((~situation(go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))) | (~at(d, go(d, s0)))) <=> ((~situation(go(d, s0))) | (~at(d, go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(195,plain,
% 0.43/0.60 (((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~situation(go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))) | (~at(d, go(d, s0))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~situation(go(d, s0))) | (~at(d, go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[194])).
% 0.43/0.60 tff(196,plain,
% 0.43/0.60 (((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~situation(go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))) | (~at(d, go(d, s0))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | (~situation(go(d, s0))) | (~at(d, go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[195, 193])).
% 0.43/0.60 tff(197,plain,
% 0.43/0.60 ((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | ((~situation(go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0))) | (~at(d, go(d, s0))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(198,plain,
% 0.43/0.60 ((~![Situation: $i] : ((~situation(Situation)) | (~warm(Situation)) | at(b, climb(b, Situation)) | (~at(d, Situation)))) | (~situation(go(d, s0))) | (~at(d, go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0)))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.43/0.60 tff(199,plain,
% 0.43/0.60 ((~situation(go(d, s0))) | (~warm(go(d, s0))) | at(b, climb(b, go(d, s0)))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[198, 192, 110])).
% 0.43/0.60 tff(200,plain,
% 0.43/0.60 ((~warm(go(d, s0))) | at(b, climb(b, go(d, s0)))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[199, 14])).
% 0.43/0.60 tff(201,plain,
% 0.43/0.60 (at(b, climb(b, go(d, s0)))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[200, 182])).
% 0.43/0.60 tff(202,plain,
% 0.43/0.60 (((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~at(b, climb(b, go(d, s0)))) | (~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | (~at(b, climb(b, go(d, s0)))) | (~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(203,plain,
% 0.43/0.60 (((~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))) | (~at(b, climb(b, go(d, s0))))) <=> ((~at(b, climb(b, go(d, s0)))) | (~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(204,plain,
% 0.43/0.60 (((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))) | (~at(b, climb(b, go(d, s0)))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~at(b, climb(b, go(d, s0)))) | (~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0))))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[203])).
% 0.43/0.60 tff(205,plain,
% 0.43/0.60 (((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))) | (~at(b, climb(b, go(d, s0)))))) <=> ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | (~at(b, climb(b, go(d, s0)))) | (~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[204, 202])).
% 0.43/0.60 tff(206,plain,
% 0.43/0.60 ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | ((~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0)))) | (~at(b, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(207,plain,
% 0.43/0.60 ((~![Situation: $i] : ((~situation(Situation)) | at(a, walk(a, Situation)) | (~at(b, Situation)))) | (~at(b, climb(b, go(d, s0)))) | (~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.43/0.60 tff(208,plain,
% 0.43/0.60 ((~situation(climb(b, go(d, s0)))) | at(a, walk(a, climb(b, go(d, s0))))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[207, 59, 201])).
% 0.43/0.60 tff(209,plain,
% 0.43/0.60 (at(a, walk(a, climb(b, go(d, s0))))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[208, 25])).
% 0.43/0.60 tff(210,plain,
% 0.43/0.60 (((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | ((~situation(walk(a, climb(b, go(d, s0))))) | (~at(a, walk(a, climb(b, go(d, s0))))))) <=> ((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | (~situation(walk(a, climb(b, go(d, s0))))) | (~at(a, walk(a, climb(b, go(d, s0))))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(211,plain,
% 0.43/0.60 ((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | ((~situation(walk(a, climb(b, go(d, s0))))) | (~at(a, walk(a, climb(b, go(d, s0))))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(212,plain,
% 0.43/0.60 ((~![S: $i] : ((~situation(S)) | (~at(a, S)))) | (~situation(walk(a, climb(b, go(d, s0))))) | (~at(a, walk(a, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.43/0.60 tff(213,plain,
% 0.43/0.60 (~situation(walk(a, climb(b, go(d, s0))))),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[212, 77, 209])).
% 0.43/0.60 tff(214,plain,
% 0.43/0.60 (((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | ((~situation(climb(b, go(d, s0)))) | situation(walk(a, climb(b, go(d, s0)))))) <=> ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | (~situation(climb(b, go(d, s0)))) | situation(walk(a, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(rewrite,[status(thm)],[])).
% 0.43/0.60 tff(215,plain,
% 0.43/0.60 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | ((~situation(climb(b, go(d, s0)))) | situation(walk(a, climb(b, go(d, s0)))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(216,plain,
% 0.43/0.60 ((~![Somewhere: $i, Situation: $i] : ((~situation(Situation)) | situation(walk(Somewhere, Situation)))) | (~situation(climb(b, go(d, s0)))) | situation(walk(a, climb(b, go(d, s0))))),
% 0.43/0.60 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.43/0.60 tff(217,plain,
% 0.43/0.60 ($false),
% 0.43/0.60 inference(unit_resolution,[status(thm)],[216, 88, 25, 213])).
% 0.43/0.60 % SZS output end Proof
% 0.43/0.60 % E exiting
%------------------------------------------------------------------------------