%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT053-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:07 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT053-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.08/0.35 % Computer : n028.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 13:27:04 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% 0.14/0.41 tff(is_aligned_type, type, (
% 0.14/0.41 is_aligned: ( $i * $i ) > $o)).
% 0.14/0.41 tff(sk2_type, type, (
% 0.14/0.41 sk2: $i)).
% 0.14/0.41 tff(sk1_type, type, (
% 0.14/0.41 sk1: $i)).
% 0.14/0.41 tff(sk3_type, type, (
% 0.14/0.41 sk3: $i)).
% 0.14/0.41 tff(dissimilar_type, type, (
% 0.14/0.41 dissimilar: ( $i * $i * $i ) > $o)).
% 0.14/0.41 tff(organization_type, type, (
% 0.14/0.41 organization: $i > $o)).
% 0.14/0.41 tff(1,assumption,(~is_aligned(sk1, sk2)), introduced(assumption)).
% 0.14/0.41 tff(2,assumption,(~dissimilar(sk1, sk3, sk2)), introduced(assumption)).
% 0.14/0.41 tff(3,assumption,(~is_aligned(sk1, sk3)), introduced(assumption)).
% 0.14/0.41 tff(4,plain,
% 0.14/0.41 ((dissimilar(sk1, sk2, sk3) | dissimilar(sk1, sk3, sk2)) <=> (dissimilar(sk1, sk2, sk3) | dissimilar(sk1, sk3, sk2))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(5,axiom,(dissimilar(sk1, sk2, sk3) | dissimilar(sk1, sk3, sk2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_7_36')).
% 0.14/0.41 tff(6,plain,
% 0.14/0.41 (dissimilar(sk1, sk2, sk3) | dissimilar(sk1, sk3, sk2)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.14/0.41 tff(7,plain,
% 0.14/0.41 (dissimilar(sk1, sk2, sk3)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[6, 2])).
% 0.14/0.41 tff(8,plain,
% 0.14/0.41 (^[B: $i, A: $i, C: $i] : refl(((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B)) <=> ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(9,plain,
% 0.14/0.41 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B)) <=> ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.14/0.41 tff(10,plain,
% 0.14/0.41 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B)) <=> ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(11,plain,
% 0.14/0.41 (^[B: $i, A: $i, C: $i] : rewrite((((~dissimilar(A, B, C)) | is_aligned(A, B)) | is_aligned(A, C)) <=> ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B)))),
% 0.14/0.41 inference(bind,[status(th)],[])).
% 0.14/0.41 tff(12,plain,
% 0.14/0.41 (![B: $i, A: $i, C: $i] : (((~dissimilar(A, B, C)) | is_aligned(A, B)) | is_aligned(A, C)) <=> ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))),
% 0.14/0.41 inference(quant_intro,[status(thm)],[11])).
% 0.14/0.41 tff(13,axiom,(![B: $i, A: $i, C: $i] : (((~dissimilar(A, B, C)) | is_aligned(A, B)) | is_aligned(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_2_30')).
% 0.14/0.41 tff(14,plain,
% 0.14/0.41 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.14/0.41 tff(15,plain,
% 0.14/0.41 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.14/0.41 tff(16,plain,(
% 0.14/0.41 ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))),
% 0.14/0.41 inference(skolemize,[status(sab)],[15])).
% 0.14/0.41 tff(17,plain,
% 0.14/0.41 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.14/0.41 tff(18,plain,
% 0.14/0.41 (((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | ((~dissimilar(sk1, sk2, sk3)) | is_aligned(sk1, sk3) | is_aligned(sk1, sk2))) <=> ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | (~dissimilar(sk1, sk2, sk3)) | is_aligned(sk1, sk3) | is_aligned(sk1, sk2))),
% 0.14/0.41 inference(rewrite,[status(thm)],[])).
% 0.14/0.41 tff(19,plain,
% 0.14/0.41 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | ((~dissimilar(sk1, sk2, sk3)) | is_aligned(sk1, sk3) | is_aligned(sk1, sk2))),
% 0.14/0.41 inference(quant_inst,[status(thm)],[])).
% 0.14/0.41 tff(20,plain,
% 0.14/0.41 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | (~dissimilar(sk1, sk2, sk3)) | is_aligned(sk1, sk3) | is_aligned(sk1, sk2)),
% 0.14/0.41 inference(modus_ponens,[status(thm)],[19, 18])).
% 0.14/0.41 tff(21,plain,
% 0.14/0.41 (is_aligned(sk1, sk3) | is_aligned(sk1, sk2)),
% 0.14/0.41 inference(unit_resolution,[status(thm)],[20, 17, 7])).
% 0.14/0.42 tff(22,plain,
% 0.14/0.42 (is_aligned(sk1, sk2)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[21, 3])).
% 0.14/0.42 tff(23,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : refl((organization(A) | (~dissimilar(A, B, C))) <=> (organization(A) | (~dissimilar(A, B, C))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(24,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C))) <=> ![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[23])).
% 0.14/0.42 tff(25,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C))) <=> ![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(26,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : rewrite(((~dissimilar(A, B, C)) | organization(A)) <=> (organization(A) | (~dissimilar(A, B, C))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(27,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | organization(A)) <=> ![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[26])).
% 0.14/0.42 tff(28,axiom,(![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | organization(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_2_29')).
% 0.14/0.42 tff(29,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.14/0.42 tff(30,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.14/0.42 tff(31,plain,(
% 0.14/0.42 ![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[30])).
% 0.14/0.42 tff(32,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.14/0.42 tff(33,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | (organization(sk1) | (~dissimilar(sk1, sk2, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | organization(sk1) | (~dissimilar(sk1, sk2, sk3)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(34,plain,
% 0.14/0.42 ((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | (organization(sk1) | (~dissimilar(sk1, sk2, sk3)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(35,plain,
% 0.14/0.42 ((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | organization(sk1) | (~dissimilar(sk1, sk2, sk3))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.14/0.42 tff(36,plain,
% 0.14/0.42 (organization(sk1)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[35, 32, 7])).
% 0.14/0.42 tff(37,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : refl((is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B)) <=> (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B)))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(38,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B)) <=> ![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[37])).
% 0.14/0.42 tff(39,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B)) <=> ![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(40,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) <=> (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))), (((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, C, B)) <=> ((is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))) | dissimilar(A, C, B)))), rewrite(((is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))) | dissimilar(A, C, B)) <=> (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))), (((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, C, B)) <=> (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(41,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, C, B)) <=> ![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[40])).
% 0.14/0.42 tff(42,axiom,(![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, C, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_2_34')).
% 0.14/0.42 tff(43,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.14/0.42 tff(44,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.14/0.42 tff(45,plain,(
% 0.14/0.42 ![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))),
% 0.14/0.42 inference(skolemize,[status(sab)],[44])).
% 0.14/0.42 tff(46,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.14/0.42 tff(47,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)))) <=> ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(48,plain,
% 0.14/0.42 ((is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)) | dissimilar(sk1, sk3, sk2)) <=> (dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(49,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)) | dissimilar(sk1, sk3, sk2))) <=> ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[48])).
% 0.14/0.42 tff(50,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)) | dissimilar(sk1, sk3, sk2))) <=> ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)))),
% 0.14/0.42 inference(transitivity,[status(thm)],[49, 47])).
% 0.14/0.42 tff(51,plain,
% 0.14/0.42 ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)) | dissimilar(sk1, sk3, sk2))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(52,plain,
% 0.14/0.42 ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.14/0.42 tff(53,plain,
% 0.14/0.42 (is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[52, 46, 2, 36])).
% 0.14/0.42 tff(54,plain,
% 0.14/0.42 ($false),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[53, 22, 3])).
% 0.14/0.42 tff(55,plain,(is_aligned(sk1, sk3) | dissimilar(sk1, sk3, sk2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.42 tff(56,plain,
% 0.14/0.42 (is_aligned(sk1, sk3)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[55, 2])).
% 0.14/0.42 tff(57,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : refl(((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B))) <=> ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(58,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[57])).
% 0.14/0.42 tff(59,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(60,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite(((~dissimilar(A, B, C)) | (~is_aligned(A, B))) <=> ((~dissimilar(A, B, C)) | (~is_aligned(A, B)))), ((((~dissimilar(A, B, C)) | (~is_aligned(A, B))) | (~is_aligned(A, C))) <=> (((~dissimilar(A, B, C)) | (~is_aligned(A, B))) | (~is_aligned(A, C))))), rewrite((((~dissimilar(A, B, C)) | (~is_aligned(A, B))) | (~is_aligned(A, C))) <=> ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))), ((((~dissimilar(A, B, C)) | (~is_aligned(A, B))) | (~is_aligned(A, C))) <=> ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(61,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (((~dissimilar(A, B, C)) | (~is_aligned(A, B))) | (~is_aligned(A, C))) <=> ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[60])).
% 0.14/0.42 tff(62,axiom,(![B: $i, A: $i, C: $i] : (((~dissimilar(A, B, C)) | (~is_aligned(A, B))) | (~is_aligned(A, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_2_31')).
% 0.14/0.42 tff(63,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.14/0.42 tff(64,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.14/0.42 tff(65,plain,(
% 0.14/0.42 ![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[64])).
% 0.14/0.42 tff(66,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.14/0.42 tff(67,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | ((~dissimilar(sk1, sk2, sk3)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | (~dissimilar(sk1, sk2, sk3)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(68,plain,
% 0.14/0.42 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | ((~dissimilar(sk1, sk2, sk3)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2)))),
% 0.14/0.42 inference(quant_inst,[status(thm)],[])).
% 0.14/0.42 tff(69,plain,
% 0.14/0.42 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | (~dissimilar(sk1, sk2, sk3)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.14/0.42 tff(70,plain,
% 0.14/0.42 ((~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2))),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[69, 66, 7])).
% 0.14/0.42 tff(71,plain,
% 0.14/0.42 (~is_aligned(sk1, sk2)),
% 0.14/0.42 inference(unit_resolution,[status(thm)],[70, 56])).
% 0.14/0.42 tff(72,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : refl((dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))) <=> (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(73,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))) <=> ![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[72])).
% 0.14/0.42 tff(74,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))) <=> ![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(75,plain,
% 0.14/0.42 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) <=> (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))), (((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, B, C)) <=> ((is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))) | dissimilar(A, B, C)))), rewrite(((is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A))) | dissimilar(A, B, C)) <=> (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))), (((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, B, C)) <=> (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))))),
% 0.14/0.42 inference(bind,[status(th)],[])).
% 0.14/0.42 tff(76,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, B, C)) <=> ![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))),
% 0.14/0.42 inference(quant_intro,[status(thm)],[75])).
% 0.14/0.42 tff(77,axiom,(![B: $i, A: $i, C: $i] : ((((~organization(A)) | (~is_aligned(A, B))) | is_aligned(A, C)) | dissimilar(A, B, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','definition_2_33')).
% 0.14/0.42 tff(78,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[77, 76])).
% 0.14/0.42 tff(79,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[78, 74])).
% 0.14/0.42 tff(80,plain,(
% 0.14/0.42 ![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))),
% 0.14/0.42 inference(skolemize,[status(sab)],[79])).
% 0.14/0.42 tff(81,plain,
% 0.14/0.42 (![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))),
% 0.14/0.42 inference(modus_ponens,[status(thm)],[80, 73])).
% 0.14/0.42 tff(82,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | (dissimilar(sk1, sk3, sk2) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))) <=> ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | dissimilar(sk1, sk3, sk2) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(83,plain,
% 0.14/0.42 ((dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1))) <=> (dissimilar(sk1, sk3, sk2) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))),
% 0.14/0.42 inference(rewrite,[status(thm)],[])).
% 0.14/0.42 tff(84,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | (dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1)))) <=> ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | (dissimilar(sk1, sk3, sk2) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1))))),
% 0.14/0.42 inference(monotonicity,[status(thm)],[83])).
% 0.14/0.42 tff(85,plain,
% 0.14/0.42 (((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | (dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1)))) <=> ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | dissimilar(sk1, sk3, sk2) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))),
% 0.14/0.43 inference(transitivity,[status(thm)],[84, 82])).
% 0.14/0.43 tff(86,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | (dissimilar(sk1, sk3, sk2) | is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(87,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | dissimilar(sk1, sk3, sk2) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.14/0.43 tff(88,plain,
% 0.14/0.43 ((~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[87, 81, 2, 36])).
% 0.14/0.43 tff(89,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[88, 71, 56])).
% 0.14/0.43 tff(90,plain,(dissimilar(sk1, sk3, sk2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.43 tff(91,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | ((~dissimilar(sk1, sk3, sk2)) | is_aligned(sk1, sk2) | is_aligned(sk1, sk3))) <=> ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | (~dissimilar(sk1, sk3, sk2)) | is_aligned(sk1, sk2) | is_aligned(sk1, sk3))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(92,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | ((~dissimilar(sk1, sk3, sk2)) | is_aligned(sk1, sk2) | is_aligned(sk1, sk3))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(93,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | is_aligned(A, C) | is_aligned(A, B))) | (~dissimilar(sk1, sk3, sk2)) | is_aligned(sk1, sk2) | is_aligned(sk1, sk3)),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[92, 91])).
% 0.14/0.43 tff(94,plain,
% 0.14/0.43 (is_aligned(sk1, sk2) | is_aligned(sk1, sk3)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[93, 17, 90])).
% 0.14/0.43 tff(95,plain,
% 0.14/0.43 (is_aligned(sk1, sk3)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[94, 1])).
% 0.14/0.43 tff(96,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | (organization(sk1) | (~dissimilar(sk1, sk3, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | organization(sk1) | (~dissimilar(sk1, sk3, sk2)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(97,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | (organization(sk1) | (~dissimilar(sk1, sk3, sk2)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(98,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (organization(A) | (~dissimilar(A, B, C)))) | organization(sk1) | (~dissimilar(sk1, sk3, sk2))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.14/0.43 tff(99,plain,
% 0.14/0.43 (organization(sk1)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[98, 32, 90])).
% 0.14/0.43 tff(100,plain,
% 0.14/0.43 (((~dissimilar(sk1, sk2, sk3)) | (~dissimilar(sk1, sk3, sk2))) <=> ((~dissimilar(sk1, sk2, sk3)) | (~dissimilar(sk1, sk3, sk2)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(101,plain,
% 0.14/0.43 (((~dissimilar(sk1, sk3, sk2)) | (~dissimilar(sk1, sk2, sk3))) <=> ((~dissimilar(sk1, sk2, sk3)) | (~dissimilar(sk1, sk3, sk2)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(102,axiom,((~dissimilar(sk1, sk3, sk2)) | (~dissimilar(sk1, sk2, sk3))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma_7_39')).
% 0.14/0.43 tff(103,plain,
% 0.14/0.43 ((~dissimilar(sk1, sk2, sk3)) | (~dissimilar(sk1, sk3, sk2))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.14/0.43 tff(104,plain,
% 0.14/0.43 ((~dissimilar(sk1, sk2, sk3)) | (~dissimilar(sk1, sk3, sk2))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[103, 100])).
% 0.14/0.43 tff(105,plain,
% 0.14/0.43 (~dissimilar(sk1, sk2, sk3)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[104, 90])).
% 0.14/0.43 tff(106,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (dissimilar(sk1, sk2, sk3) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))) <=> ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | dissimilar(sk1, sk2, sk3) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(107,plain,
% 0.14/0.43 ((is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1)) | dissimilar(sk1, sk2, sk3)) <=> (dissimilar(sk1, sk2, sk3) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(108,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1)) | dissimilar(sk1, sk2, sk3))) <=> ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (dissimilar(sk1, sk2, sk3) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[107])).
% 0.14/0.43 tff(109,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1)) | dissimilar(sk1, sk2, sk3))) <=> ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | dissimilar(sk1, sk2, sk3) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1)))),
% 0.14/0.43 inference(transitivity,[status(thm)],[108, 106])).
% 0.14/0.43 tff(110,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | (is_aligned(sk1, sk2) | (~is_aligned(sk1, sk3)) | (~organization(sk1)) | dissimilar(sk1, sk2, sk3))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(111,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)) | dissimilar(A, C, B))) | dissimilar(sk1, sk2, sk3) | (~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2) | (~organization(sk1))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.14/0.43 tff(112,plain,
% 0.14/0.43 ((~is_aligned(sk1, sk3)) | is_aligned(sk1, sk2)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[111, 46, 105, 99])).
% 0.14/0.43 tff(113,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[112, 95, 1])).
% 0.14/0.43 tff(114,plain,(is_aligned(sk1, sk2)), inference(lemma,lemma(discharge,[]))).
% 0.14/0.43 tff(115,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | ((~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | (~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(116,plain,
% 0.14/0.43 (((~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk2)) | (~is_aligned(sk1, sk3))) <=> ((~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(117,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | ((~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk2)) | (~is_aligned(sk1, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | ((~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2))))),
% 0.14/0.43 inference(monotonicity,[status(thm)],[116])).
% 0.14/0.43 tff(118,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | ((~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk2)) | (~is_aligned(sk1, sk3)))) <=> ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | (~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2)))),
% 0.14/0.43 inference(transitivity,[status(thm)],[117, 115])).
% 0.14/0.43 tff(119,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | ((~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk2)) | (~is_aligned(sk1, sk3)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(120,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : ((~dissimilar(A, B, C)) | (~is_aligned(A, C)) | (~is_aligned(A, B)))) | (~dissimilar(sk1, sk3, sk2)) | (~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[119, 118])).
% 0.14/0.43 tff(121,plain,
% 0.14/0.43 ((~is_aligned(sk1, sk3)) | (~is_aligned(sk1, sk2))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[120, 66, 90])).
% 0.14/0.43 tff(122,plain,
% 0.14/0.43 (~is_aligned(sk1, sk3)),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[121, 114])).
% 0.14/0.43 tff(123,plain,
% 0.14/0.43 (((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | (dissimilar(sk1, sk2, sk3) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)))) <=> ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | dissimilar(sk1, sk2, sk3) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)))),
% 0.14/0.43 inference(rewrite,[status(thm)],[])).
% 0.14/0.43 tff(124,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | (dissimilar(sk1, sk2, sk3) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1)))),
% 0.14/0.43 inference(quant_inst,[status(thm)],[])).
% 0.14/0.43 tff(125,plain,
% 0.14/0.43 ((~![B: $i, A: $i, C: $i] : (dissimilar(A, B, C) | is_aligned(A, C) | (~is_aligned(A, B)) | (~organization(A)))) | dissimilar(sk1, sk2, sk3) | is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2)) | (~organization(sk1))),
% 0.14/0.43 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.14/0.43 tff(126,plain,
% 0.14/0.43 (is_aligned(sk1, sk3) | (~is_aligned(sk1, sk2))),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[125, 81, 105, 99])).
% 0.14/0.43 tff(127,plain,
% 0.14/0.43 ($false),
% 0.14/0.43 inference(unit_resolution,[status(thm)],[126, 122, 114])).
% 0.14/0.43 % SZS output end Proof
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------