%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU040+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:26:49 AM UTC 2025
% Result : Theorem 1.31s 1.47s
% Output : Proof 1.31s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : SEU040+1 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 05:58:32 EDT 2025
% 0.14/0.37 % CPUTime :
% 1.31/1.47 % SZS status Theorem
% 1.31/1.47 % SZS output start Proof
% 1.31/1.47 tff(subset_type, type, (
% 1.31/1.47 subset: ( $i * $i ) > $o)).
% 1.31/1.47 tff(relation_dom_type, type, (
% 1.31/1.47 relation_dom: $i > $i)).
% 1.31/1.47 tff(relation_dom_restriction_type, type, (
% 1.31/1.47 relation_dom_restriction: ( $i * $i ) > $i)).
% 1.31/1.47 tff(relation_type, type, (
% 1.31/1.47 relation: $i > $o)).
% 1.31/1.47 tff(tptp_fun_B_11_type, type, (
% 1.31/1.47 tptp_fun_B_11: $i)).
% 1.31/1.47 tff(tptp_fun_A_12_type, type, (
% 1.31/1.47 tptp_fun_A_12: $i)).
% 1.31/1.47 tff(relation_rng_type, type, (
% 1.31/1.47 relation_rng: $i > $i)).
% 1.31/1.47 tff(function_type, type, (
% 1.31/1.47 function: $i > $o)).
% 1.31/1.47 tff(1,plain,
% 1.31/1.47 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B))) <=> ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(2,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[1])).
% 1.31/1.47 tff(3,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(4,plain,
% 1.31/1.47 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B))) <=> ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(5,plain,
% 1.31/1.47 (![A: $i, B: $i] : (relation(B) => subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[4])).
% 1.31/1.47 tff(6,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t89_relat_1')).
% 1.31/1.47 tff(7,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[6, 5])).
% 1.31/1.47 tff(8,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[7, 3])).
% 1.31/1.47 tff(9,plain,(
% 1.31/1.47 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))),
% 1.31/1.47 inference(skolemize,[status(sab)],[8])).
% 1.31/1.47 tff(10,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[9, 2])).
% 1.31/1.47 tff(11,plain,
% 1.31/1.47 (^[A: $i, B: $i] : refl(((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(12,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[11])).
% 1.31/1.47 tff(13,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(14,plain,
% 1.31/1.47 (^[A: $i, B: $i] : rewrite((relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 1.31/1.47 inference(bind,[status(th)],[])).
% 1.31/1.47 tff(15,plain,
% 1.31/1.47 (![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))) <=> ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 1.31/1.47 inference(quant_intro,[status(thm)],[14])).
% 1.31/1.47 tff(16,axiom,(![A: $i, B: $i] : (relation(B) => subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t99_relat_1')).
% 1.31/1.47 tff(17,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[16, 15])).
% 1.31/1.47 tff(18,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[17, 13])).
% 1.31/1.47 tff(19,plain,(
% 1.31/1.47 ![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 1.31/1.47 inference(skolemize,[status(sab)],[18])).
% 1.31/1.47 tff(20,plain,
% 1.31/1.47 (![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[19, 12])).
% 1.31/1.47 tff(21,assumption,(~subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))), introduced(assumption)).
% 1.31/1.47 tff(22,plain,
% 1.31/1.47 ((~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))) <=> (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(23,plain,
% 1.31/1.47 ((~![A: $i, B: $i] : ((relation(B) & function(B)) => (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))) <=> (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(24,axiom,(~![A: $i, B: $i] : ((relation(B) & function(B)) => (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t76_funct_1')).
% 1.31/1.47 tff(25,plain,
% 1.31/1.47 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.31/1.47 tff(26,plain,
% 1.31/1.47 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[25, 22])).
% 1.31/1.47 tff(27,plain,
% 1.31/1.47 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[26, 22])).
% 1.31/1.47 tff(28,plain,
% 1.31/1.47 (~![A: $i, B: $i] : ((~(relation(B) & function(B))) | (subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)) & subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B))))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[27, 22])).
% 1.31/1.47 tff(29,plain,(
% 1.31/1.47 ~((~(relation(B!11) & function(B!11))) | (subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)) & subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))))),
% 1.31/1.47 inference(skolemize,[status(sab)],[28])).
% 1.31/1.47 tff(30,plain,
% 1.31/1.47 (relation(B!11) & function(B!11)),
% 1.31/1.47 inference(or_elim,[status(thm)],[29])).
% 1.31/1.47 tff(31,plain,
% 1.31/1.47 (relation(B!11)),
% 1.31/1.47 inference(and_elim,[status(thm)],[30])).
% 1.31/1.47 tff(32,plain,
% 1.31/1.47 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | ((~relation(B!11)) | subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | (~relation(B!11)) | subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(33,plain,
% 1.31/1.47 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | ((~relation(B!11)) | subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.47 tff(34,plain,
% 1.31/1.47 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_rng(relation_dom_restriction(B, A)), relation_rng(B)))) | (~relation(B!11)) | subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 1.31/1.47 tff(35,plain,
% 1.31/1.47 ($false),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[34, 31, 21, 20])).
% 1.31/1.47 tff(36,plain,(subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))), inference(lemma,lemma(discharge,[]))).
% 1.31/1.47 tff(37,plain,
% 1.31/1.47 ((~(~((~subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))) | (~subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))))) <=> ((~subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))) | (~subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(38,plain,
% 1.31/1.47 ((subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)) & subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))) <=> (~((~subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))) | (~subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(39,plain,
% 1.31/1.47 ((~(subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)) & subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))) <=> (~(~((~subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))) | (~subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))))))),
% 1.31/1.47 inference(monotonicity,[status(thm)],[38])).
% 1.31/1.47 tff(40,plain,
% 1.31/1.47 ((~(subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)) & subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))) <=> ((~subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))) | (~subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11))))),
% 1.31/1.47 inference(transitivity,[status(thm)],[39, 37])).
% 1.31/1.47 tff(41,plain,
% 1.31/1.47 (~(subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)) & subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))),
% 1.31/1.47 inference(or_elim,[status(thm)],[29])).
% 1.31/1.47 tff(42,plain,
% 1.31/1.47 ((~subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))) | (~subset(relation_rng(relation_dom_restriction(B!11, A!12)), relation_rng(B!11)))),
% 1.31/1.47 inference(modus_ponens,[status(thm)],[41, 40])).
% 1.31/1.47 tff(43,plain,
% 1.31/1.47 (~subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))),
% 1.31/1.47 inference(unit_resolution,[status(thm)],[42, 36])).
% 1.31/1.47 tff(44,plain,
% 1.31/1.47 (((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))) | ((~relation(B!11)) | subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)))) <=> ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))) | (~relation(B!11)) | subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)))),
% 1.31/1.47 inference(rewrite,[status(thm)],[])).
% 1.31/1.47 tff(45,plain,
% 1.31/1.47 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))) | ((~relation(B!11)) | subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11)))),
% 1.31/1.47 inference(quant_inst,[status(thm)],[])).
% 1.31/1.48 tff(46,plain,
% 1.31/1.48 ((~![A: $i, B: $i] : ((~relation(B)) | subset(relation_dom(relation_dom_restriction(B, A)), relation_dom(B)))) | (~relation(B!11)) | subset(relation_dom(relation_dom_restriction(B!11, A!12)), relation_dom(B!11))),
% 1.31/1.48 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.31/1.48 tff(47,plain,
% 1.31/1.48 ($false),
% 1.31/1.48 inference(unit_resolution,[status(thm)],[46, 31, 43, 10])).
% 1.31/1.48 % SZS output end Proof
% 1.31/1.48 % E exiting
%------------------------------------------------------------------------------