%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n004.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 : Fri Sep 25 01:30:56 PM UTC 2026
% Result : Unsatisfiable 202.94s 31.62s
% Output : CNFRefutation 202.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 124 ( 124 unt; 4 def)
% Number of atoms : 233 ( 123 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 4 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 172 ( 0 sgn 172 !; 0 ?; 138 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : multiply(identity,X0) = X0,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).
fof(f2,axiom,
! [X0] : multiply(inverse(X0),X0) = identity,
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
fof(f3,plain,
! [X0] : identity = multiply(inverse(X0),X0),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X2,X0,X1] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).
fof(f5,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_of_identity) ).
fof(f6,plain,
identity = inverse(identity),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] : inverse(inverse(X0)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_involution) ).
fof(f8,axiom,
! [X0,X1] : inverse(multiply(X0,X1)) = multiply(inverse(X1),inverse(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_product_lemma) ).
fof(f11,axiom,
! [X0,X1] : intersection(X0,X1) = intersection(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_commutative) ).
fof(f12,axiom,
! [X0,X1] : union(X0,X1) = union(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_commutative) ).
fof(f13,axiom,
! [X2,X0,X1] : intersection(X0,intersection(X1,X2)) = intersection(intersection(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_associative) ).
fof(f14,axiom,
! [X2,X0,X1] : union(X0,union(X1,X2)) = union(union(X0,X1),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_associative) ).
fof(f15,axiom,
! [X0,X1] : union(intersection(X0,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_intersection_absorbtion) ).
fof(f16,axiom,
! [X0,X1] : intersection(union(X0,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_union_absorbtion) ).
fof(f17,axiom,
! [X2,X0,X1] : multiply(X0,union(X1,X2)) = union(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_union1) ).
fof(f18,axiom,
! [X2,X0,X1] : multiply(X0,intersection(X1,X2)) = intersection(multiply(X0,X1),multiply(X0,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_intersection1) ).
fof(f19,axiom,
! [X2,X0,X1] : multiply(union(X0,X1),X2) = union(multiply(X0,X2),multiply(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_union2) ).
fof(f21,axiom,
! [X0] : positive_part(X0) = union(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',positive_part) ).
fof(f22,axiom,
! [X0] : negative_part(X0) = intersection(X0,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',negative_part) ).
fof(f23,negated_conjecture,
multiply(positive_part(a),negative_part(a)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_product) ).
fof(f24,plain,
a != multiply(positive_part(a),negative_part(a)),
inference(reorient_equations,[],[f23]) ).
fof(f25,plain,
a != multiply(union(a,identity),intersection(a,identity)),
inference(definition_unfolding,[],[f24,f21,f22]) ).
tcf(c_70,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[],[f3]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_73,plain,
inverse(identity) = identity,
inference(cnf_transformation,[],[f6]) ).
tcf(c_74,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(cnf_transformation,[],[f7]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(cnf_transformation,[],[f11]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[],[f12]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] : union(intersection(X0,X1),X1) = X1,
inference(cnf_transformation,[],[f15]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] : intersection(union(X0,X1),X1) = X1,
inference(cnf_transformation,[],[f16]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i,X2: $i] : union(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,union(X1,X2)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,intersection(X1,X2)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] : union(multiply(X0,X1),multiply(X2,X1)) = multiply(union(X0,X2),X1),
inference(cnf_transformation,[],[f19]) ).
tcf(c_88,negated_conjecture,
multiply(union(a,identity),intersection(a,identity)) != a,
inference(cnf_transformation,[],[f25]) ).
tcf(c_106,plain,
! [X0: $i,X1: $i] : union(X0,intersection(X1,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_82,c_81,c_79,c_80,c_78]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] : intersection(X0,union(X1,X0)) = X0,
inference(theory_normalisation,[status(thm)],[c_83,c_81,c_79,c_80,c_78]) ).
tcf(c_108,negated_conjecture,
multiply(union(identity,a),intersection(identity,a)) != a,
inference(theory_normalisation,[status(thm)],[c_88,c_81,c_79,c_80,c_78]) ).
tcf(c_155,definition,
iPr_def_10 = union(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_156,definition,
iPr_def_11 = intersection(identity,a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_157,definition,
iPr_def_12 = multiply(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_158,definition,
iPr_def_13 = inverse(identity),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_159,negated_conjecture,
iPr_def_12 != a,
inference(demodulation,[status(thm)],[c_108,c_156,c_155,c_157]) ).
tcf(c_160,plain,
! [X0: $i,X1: $i] : intersection(X0,union(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_107]) ).
tcf(c_161,plain,
! [X0: $i,X1: $i] : union(X0,intersection(X1,X0)) = X0,
inference(demodulation,[status(thm)],[c_106]) ).
tcf(c_162,plain,
! [X0: $i,X1: $i,X2: $i] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(demodulation,[status(thm)],[c_72]) ).
tcf(c_163,plain,
! [X0: $i] : multiply(inverse(X0),X0) = identity,
inference(demodulation,[status(thm)],[c_71]) ).
tcf(c_164,plain,
! [X0: $i] : multiply(identity,X0) = X0,
inference(demodulation,[status(thm)],[c_70]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] : union(multiply(X0,X1),multiply(X2,X1)) = multiply(union(X0,X2),X1),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_167,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,intersection(X1,X2)),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_168,plain,
! [X0: $i,X1: $i,X2: $i] : union(multiply(X0,X1),multiply(X0,X2)) = multiply(X0,union(X1,X2)),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i,X2: $i] : union(union(X0,X1),X2) = union(X0,union(X1,X2)),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_170,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(intersection(X0,X1),X2) = intersection(X0,intersection(X1,X2)),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i] : union(X0,X1) = union(X1,X0),
inference(demodulation,[status(thm)],[c_79]) ).
tcf(c_172,plain,
! [X0: $i,X1: $i] : intersection(X0,X1) = intersection(X1,X0),
inference(demodulation,[status(thm)],[c_78]) ).
tcf(c_175,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),inverse(X1)) = inverse(multiply(X1,X0)),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_176,plain,
! [X0: $i] : inverse(inverse(X0)) = X0,
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_177,plain,
iPr_def_13 = identity,
inference(demodulation,[status(thm)],[c_73,c_158]) ).
tcf(c_263,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,intersection(X1,X2)) = intersection(X1,intersection(X0,X2)),
inference(superposition,[status(thm)],[c_170,c_172]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i,X2: $i] : union(X0,union(X1,X2)) = union(X1,union(X0,X2)),
inference(superposition,[status(thm)],[c_169,c_171]) ).
tcf(c_270,plain,
union(iPr_def_13,a) = iPr_def_10,
inference(superposition,[status(thm)],[c_177,c_155]) ).
tcf(c_271,plain,
intersection(iPr_def_13,a) = iPr_def_11,
inference(superposition,[status(thm)],[c_177,c_156]) ).
tcf(c_272,plain,
! [X0: $i] : multiply(iPr_def_13,X0) = X0,
inference(superposition,[status(thm)],[c_177,c_164]) ).
tcf(c_276,plain,
inverse(iPr_def_13) = identity,
inference(superposition,[status(thm)],[c_158,c_176]) ).
tcf(c_279,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = identity,
inference(superposition,[status(thm)],[c_176,c_163]) ).
tcf(c_295,plain,
! [X0: $i,X1: $i] : intersection(X0,union(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_171,c_160]) ).
tcf(c_299,plain,
! [X0: $i,X1: $i] : union(X0,intersection(X0,X1)) = X0,
inference(superposition,[status(thm)],[c_172,c_161]) ).
tcf(c_306,plain,
! [X0: $i] : inverse(multiply(identity,X0)) = multiply(inverse(X0),iPr_def_13),
inference(superposition,[status(thm)],[c_158,c_175]) ).
tcf(c_308,plain,
! [X0: $i] : inverse(multiply(X0,inverse(X0))) = identity,
inference(superposition,[status(thm)],[c_175,c_163]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = multiply(identity,X1),
inference(superposition,[status(thm)],[c_163,c_162]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i,X2: $i] : intersection(X0,union(X1,union(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_169,c_160]) ).
tcf(c_345,plain,
! [X0: $i,X1: $i,X2: $i] : union(X0,intersection(X1,intersection(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_170,c_161]) ).
tcf(c_354,plain,
! [X0: $i] : intersection(identity,intersection(X0,a)) = intersection(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_156,c_263]) ).
tcf(c_366,plain,
! [X0: $i] : union(identity,union(X0,a)) = union(X0,iPr_def_10),
inference(superposition,[status(thm)],[c_155,c_264]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i] : union(X0,multiply(X1,X0)) = multiply(union(identity,X1),X0),
inference(superposition,[status(thm)],[c_164,c_166]) ).
tcf(c_398,plain,
! [X0: $i] : multiply(union(iPr_def_10,X0),iPr_def_11) = union(iPr_def_12,multiply(X0,iPr_def_11)),
inference(superposition,[status(thm)],[c_157,c_166]) ).
tcf(c_403,plain,
! [X0: $i] : multiply(union(X0,iPr_def_10),iPr_def_11) = union(multiply(X0,iPr_def_11),iPr_def_12),
inference(superposition,[status(thm)],[c_157,c_166]) ).
tcf(c_471,plain,
! [X0: $i] : multiply(iPr_def_10,intersection(iPr_def_11,X0)) = intersection(iPr_def_12,multiply(iPr_def_10,X0)),
inference(superposition,[status(thm)],[c_157,c_167]) ).
tcf(c_476,plain,
! [X0: $i] : multiply(iPr_def_10,intersection(X0,iPr_def_11)) = intersection(multiply(iPr_def_10,X0),iPr_def_12),
inference(superposition,[status(thm)],[c_157,c_167]) ).
tcf(c_571,plain,
inverse(iPr_def_13) = iPr_def_13,
inference(demodulation,[status(thm)],[c_276,c_177]) ).
tcf(c_575,plain,
! [X0: $i] : multiply(X0,inverse(X0)) = iPr_def_13,
inference(demodulation,[status(thm)],[c_279,c_177]) ).
tcf(c_576,plain,
identity = iPr_def_13,
inference(demodulation,[status(thm)],[c_308,c_571,c_575]) ).
tcf(c_577,plain,
! [X0: $i] : union(iPr_def_13,union(X0,a)) = union(X0,iPr_def_10),
inference(demodulation,[status(thm)],[c_366,c_576]) ).
tcf(c_579,plain,
! [X0: $i] : intersection(iPr_def_13,intersection(X0,a)) = intersection(X0,iPr_def_11),
inference(demodulation,[status(thm)],[c_354,c_576]) ).
tcf(c_583,plain,
! [X0: $i] : multiply(inverse(X0),iPr_def_13) = inverse(X0),
inference(demodulation,[status(thm)],[c_306,c_272,c_576]) ).
tcf(c_587,plain,
! [X0: $i,X1: $i] : multiply(inverse(X0),multiply(X0,X1)) = X1,
inference(demodulation,[status(thm)],[c_317,c_272,c_576]) ).
tcf(c_589,plain,
! [X0: $i] : multiply(iPr_def_10,intersection(X0,iPr_def_11)) = intersection(iPr_def_12,multiply(iPr_def_10,X0)),
inference(theory_normalisation,[status(thm)],[c_476,c_170,c_172,c_169,c_171]) ).
tcf(c_590,plain,
! [X0: $i] : multiply(union(X0,iPr_def_10),iPr_def_11) = union(iPr_def_12,multiply(X0,iPr_def_11)),
inference(theory_normalisation,[status(thm)],[c_403,c_170,c_172,c_169,c_171]) ).
tcf(c_593,plain,
! [X0: $i,X1: $i] : union(X0,multiply(X1,X0)) = multiply(union(iPr_def_13,X1),X0),
inference(demodulation,[status(thm)],[c_395,c_576]) ).
tcf(c_1009,plain,
! [X0: $i] : multiply(X0,iPr_def_13) = X0,
inference(superposition,[status(thm)],[c_176,c_583]) ).
tcf(c_1059,plain,
! [X0: $i,X1: $i] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(superposition,[status(thm)],[c_176,c_587]) ).
tcf(c_1066,plain,
multiply(inverse(iPr_def_10),iPr_def_12) = iPr_def_11,
inference(superposition,[status(thm)],[c_157,c_587]) ).
tcf(c_1257,plain,
! [X0: $i] : intersection(a,union(X0,iPr_def_10)) = a,
inference(superposition,[status(thm)],[c_577,c_329]) ).
tcf(c_1268,plain,
! [X0: $i] : union(iPr_def_13,intersection(X0,iPr_def_11)) = iPr_def_13,
inference(superposition,[status(thm)],[c_579,c_299]) ).
tcf(c_1277,plain,
! [X0: $i] : union(a,intersection(X0,iPr_def_11)) = a,
inference(superposition,[status(thm)],[c_579,c_345]) ).
tcf(c_1880,plain,
! [X0: $i] : union(iPr_def_12,multiply(intersection(X0,iPr_def_10),iPr_def_11)) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_161,c_398]) ).
tcf(c_1988,plain,
! [X0: $i] : union(iPr_def_12,multiply(intersection(X0,iPr_def_10),iPr_def_11)) = iPr_def_12,
inference(demodulation,[status(thm)],[c_1880,c_157]) ).
tcf(c_2890,plain,
! [X0: $i,X1: $i] : union(X0,multiply(X0,X1)) = multiply(X0,union(iPr_def_13,X1)),
inference(superposition,[status(thm)],[c_1009,c_168]) ).
tcf(c_2891,plain,
! [X0: $i,X1: $i] : intersection(X0,multiply(X0,X1)) = multiply(X0,intersection(iPr_def_13,X1)),
inference(superposition,[status(thm)],[c_1009,c_167]) ).
tcf(c_3019,plain,
! [X0: $i,X1: $i] : intersection(a,intersection(union(X0,iPr_def_10),X1)) = intersection(a,X1),
inference(superposition,[status(thm)],[c_1257,c_170]) ).
tcf(c_3052,plain,
! [X0: $i,X1: $i] : union(a,union(intersection(X0,iPr_def_11),X1)) = union(a,X1),
inference(superposition,[status(thm)],[c_1277,c_169]) ).
tcf(c_3322,plain,
multiply(iPr_def_10,iPr_def_11) = iPr_def_12,
inference(superposition,[status(thm)],[c_1066,c_1059]) ).
tcf(c_14367,plain,
! [X0: $i] : intersection(iPr_def_12,multiply(iPr_def_10,union(X0,iPr_def_11))) = multiply(iPr_def_10,iPr_def_11),
inference(superposition,[status(thm)],[c_160,c_471]) ).
tcf(c_14504,plain,
! [X0: $i] : intersection(iPr_def_12,multiply(iPr_def_10,union(X0,iPr_def_11))) = iPr_def_12,
inference(demodulation,[status(thm)],[c_14367,c_3322]) ).
tcf(c_16201,plain,
! [X0: $i] : union(X0,multiply(a,X0)) = multiply(iPr_def_10,X0),
inference(superposition,[status(thm)],[c_270,c_593]) ).
tcf(c_16221,plain,
! [X0: $i,X1: $i] : intersection(X0,multiply(union(iPr_def_13,X1),X0)) = X0,
inference(superposition,[status(thm)],[c_593,c_295]) ).
tcf(c_18953,plain,
! [X0: $i,X1: $i] : intersection(X0,multiply(union(X1,iPr_def_10),X0)) = X0,
inference(superposition,[status(thm)],[c_577,c_16221]) ).
tcf(c_104592,plain,
! [X0: $i,X1: $i] : union(X0,multiply(X0,intersection(X1,iPr_def_11))) = multiply(X0,iPr_def_13),
inference(superposition,[status(thm)],[c_1268,c_2890]) ).
tcf(c_104818,plain,
! [X0: $i,X1: $i] : union(X0,multiply(X0,intersection(X1,iPr_def_11))) = X0,
inference(demodulation,[status(thm)],[c_104592,c_1009]) ).
tcf(c_155544,plain,
! [X0: $i] : intersection(X0,multiply(X0,a)) = multiply(X0,iPr_def_11),
inference(superposition,[status(thm)],[c_271,c_2891]) ).
tcf(c_167867,plain,
! [X0: $i] : intersection(a,multiply(union(X0,iPr_def_10),a)) = intersection(a,multiply(union(X0,iPr_def_10),iPr_def_11)),
inference(superposition,[status(thm)],[c_155544,c_3019]) ).
tcf(c_168059,plain,
! [X0: $i] : intersection(a,union(iPr_def_12,multiply(X0,iPr_def_11))) = a,
inference(demodulation,[status(thm)],[c_167867,c_590,c_18953]) ).
tcf(c_169522,plain,
intersection(a,iPr_def_12) = a,
inference(superposition,[status(thm)],[c_1988,c_168059]) ).
tcf(c_170831,plain,
intersection(iPr_def_12,a) = a,
inference(theory_normalisation,[status(thm)],[c_169522,c_170,c_172,c_169,c_171]) ).
tcf(c_172208,plain,
union(iPr_def_12,a) = iPr_def_12,
inference(superposition,[status(thm)],[c_170831,c_299]) ).
tcf(c_173259,plain,
! [X0: $i] : union(a,multiply(a,intersection(X0,iPr_def_11))) = union(a,multiply(iPr_def_10,intersection(X0,iPr_def_11))),
inference(superposition,[status(thm)],[c_16201,c_3052]) ).
tcf(c_173466,plain,
! [X0: $i] : union(a,intersection(iPr_def_12,multiply(iPr_def_10,X0))) = a,
inference(demodulation,[status(thm)],[c_173259,c_589,c_104818]) ).
tcf(c_176486,plain,
union(a,iPr_def_12) = a,
inference(superposition,[status(thm)],[c_14504,c_173466]) ).
tcf(c_176857,plain,
union(iPr_def_12,a) = a,
inference(theory_normalisation,[status(thm)],[c_176486,c_170,c_172,c_169,c_171]) ).
tcf(c_176858,plain,
a = iPr_def_12,
inference(demodulation,[status(thm)],[c_176857,c_172208]) ).
tcf(c_177499,plain,
$false,
inference(superposition,[status(thm)],[c_176858,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP114-1 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.58 % Computer : n004.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Wed Sep 23 13:34:09 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.62 Running UEQ theorem proving
% 0.10/0.62 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.63
% 0.10/0.63 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.63
% 0.15/0.63 % Detected problem language: tptp
% 0.15/0.64 % Proving...
% 202.94/31.62 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 202.94/31.62 % SZS status Started for theBenchmark.p
% 202.94/31.62 % SZS status Unsatisfiable for theBenchmark.p
% 202.94/31.62
% 202.94/31.62 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 202.94/31.62
% 202.94/31.62 % ------ iProver source info
% 202.94/31.62
% 202.94/31.62 % git: date: 2026-07-19 20:42:38 +0200
% 202.94/31.62 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 202.94/31.62 % git: non_committed_changes: false
% 202.94/31.62
% 202.94/31.62 % ------ Parsing...% successful
% 202.94/31.62
% 202.94/31.62
% 202.94/31.62 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 202.94/31.62
% 202.94/31.62 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 202.94/31.62
% 202.94/31.62 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 202.94/31.62
% 202.94/31.62 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 202.94/31.62 % ------ Proving...
% 202.94/31.62 % ------ Problem Properties
% 202.94/31.62
% 202.94/31.62 %
% 202.94/31.62 % clauses 23
% 202.94/31.62 % conjectures 1
% 202.94/31.62 % EPR 2
% 202.94/31.62 % Horn 23
% 202.94/31.62 % unary 23
% 202.94/31.62 % binary 0
% 202.94/31.62 % lits 23
% 202.94/31.62 % lits eq 23
% 202.94/31.62 % fd_pure 0
% 202.94/31.62 % fd_pseudo 0
% 202.94/31.62 % fd_cond 0
% 202.94/31.62 % fd_pseudo_cond 0
% 202.94/31.62 % AC symbols 2
% 202.94/31.62
% 202.94/31.62 % ------ Input Options Time Limit: Unbounded
% 202.94/31.62
% 202.94/31.62
% 202.94/31.62 % ------
% 202.94/31.62 % Current options:
% 202.94/31.62 % ------
% 202.94/31.62
% 202.94/31.62
% 202.94/31.62 %
% 202.94/31.62
% 202.94/31.62 % ------ Proving...
% 202.94/31.62 %
% 202.94/31.62
% 202.94/31.62 % SZS status Unsatisfiable for theBenchmark.p
% 202.94/31.62
% 202.94/31.62 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 202.94/31.62
% 202.94/31.62
%------------------------------------------------------------------------------