%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n019.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 12:53:09 PM UTC 2026
% Result : Unsatisfiable 9.25s 12.44s
% Output : CNFRefutation 9.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 118 ( 118 unt; 0 def)
% Number of atoms : 167 ( 117 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 296 ( 0 sgn 296 !; 0 ?; 285 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : difference(X0,difference(X1,X0)) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
fof(f2,axiom,
! [X0,X1] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
fof(f3,axiom,
! [X2,X0,X1] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),difference(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).
fof(f4,axiom,
! [X0,X1] : multiply(X0,X1) = difference(X0,difference(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
fof(f5,plain,
! [X0,X1] : difference(X0,difference(X0,X1)) = multiply(X0,X1),
inference(reorient_equations,[],[f4]) ).
fof(f6,negated_conjecture,
multiply(multiply(a,b),c) != multiply(a,multiply(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_multiply) ).
fof(f7,plain,
difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c)) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(definition_unfolding,[],[f6,f5,f5,f5,f5]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X1,X0)) = X0,
inference(cnf_transformation,[],[f1]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,X1)) = difference(X1,difference(X1,X0)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X2,X1)) = difference(difference(X0,X2),X1),
inference(cnf_transformation,[],[f3]) ).
tcf(c_57,negated_conjecture,
difference(difference(a,difference(a,b)),difference(difference(a,difference(a,b)),c)) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),X1) = difference(X0,X1),
inference(superposition,[status(thm)],[c_54,c_54]) ).
tcf(c_66,plain,
difference(a,difference(a,difference(b,difference(b,c)))) != difference(c,difference(c,difference(a,difference(a,b)))),
inference(demodulation,[status(thm)],[c_57,c_55]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),difference(X1,difference(X1,X0))) = difference(X0,X1),
inference(superposition,[status(thm)],[c_55,c_54]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),difference(X0,X1)) = difference(X1,difference(X1,difference(X0,X1))),
inference(superposition,[status(thm)],[c_64,c_55]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X2,X0)) = difference(X0,difference(X1,difference(X2,X0))),
inference(superposition,[status(thm)],[c_54,c_56]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X0,X1)),difference(X2,difference(X1,X0))) = difference(difference(X1,X2),difference(X1,X0)),
inference(superposition,[status(thm)],[c_55,c_56]) ).
tcf(c_86,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X2) = difference(difference(X0,X2),difference(X1,X2)),
inference(superposition,[status(thm)],[c_64,c_56]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X0,X1)),X1) = difference(X1,difference(X1,difference(X0,X1))),
inference(superposition,[status(thm)],[c_56,c_55]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X0,X1)),X1) = difference(X1,X1),
inference(demodulation,[status(thm)],[c_92,c_54]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X2) = difference(difference(X0,X1),X2),
inference(demodulation,[status(thm)],[c_86,c_56]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = difference(X1,X1),
inference(demodulation,[status(thm)],[c_74,c_54,c_56]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X0),X1),X2) = difference(difference(X2,X2),difference(X1,X2)),
inference(superposition,[status(thm)],[c_98,c_56]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X1)),X2) = difference(difference(X0,X2),difference(X2,X2)),
inference(superposition,[status(thm)],[c_98,c_56]) ).
tcf(c_122,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),difference(X0,X1)) = difference(difference(X1,X0),X1),
inference(superposition,[status(thm)],[c_98,c_56]) ).
tcf(c_127,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X0),difference(X1,X2)) = difference(difference(X1,X1),X2),
inference(superposition,[status(thm)],[c_98,c_56]) ).
tcf(c_129,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X0),X1) = difference(difference(X2,X2),X1),
inference(superposition,[status(thm)],[c_98,c_98]) ).
tcf(c_192,plain,
! [X0: $i,X1: $i] : difference(difference(difference(X0,X1),difference(X0,X1)),X1) = difference(X1,X1),
inference(superposition,[status(thm)],[c_64,c_95]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i] : difference(difference(difference(X0,X1),X1),difference(X1,X1)) = difference(difference(X0,X1),X1),
inference(superposition,[status(thm)],[c_54,c_68]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X1,X0)),difference(difference(X1,X0),difference(X1,X0))) = difference(X0,difference(X1,X0)),
inference(superposition,[status(thm)],[c_64,c_68]) ).
tcf(c_224,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X1,X1)),difference(difference(X1,X1),difference(X0,X0))) = difference(X0,difference(X1,X1)),
inference(superposition,[status(thm)],[c_98,c_68]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i] : difference(difference(difference(X0,X1),difference(X0,X1)),difference(X1,difference(X1,X0))) = difference(difference(X1,difference(X1,X0)),difference(X1,difference(X1,X0))),
inference(superposition,[status(thm)],[c_68,c_95]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),difference(X1,difference(X1,X0))) = difference(difference(X0,X1),difference(X2,difference(X1,difference(X1,X0)))),
inference(superposition,[status(thm)],[c_68,c_56]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = iPr_def_10(X1),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_129]) ).
tcf(c_236,plain,
! [X0: $i] : difference(X0,X0) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_192,c_232]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i] : iPr_def_10(difference(X0,X1)) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_127,c_232]) ).
tcf(c_240,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),X0) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_122,c_236,c_239]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] : difference(difference(difference(X0,X1),X1),iPr_def_10(X1)) = difference(difference(X0,X1),X1),
inference(demodulation,[status(thm)],[c_216,c_236]) ).
tcf(c_242,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),iPr_def_10(X1)) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_241,c_64]) ).
tcf(c_247,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,iPr_def_10(X1)),X2) = difference(X0,X2),
inference(demodulation,[status(thm)],[c_121,c_236,c_242]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] : difference(iPr_def_10(X0),X1) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_118,c_232,c_239]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] : difference(X0,iPr_def_10(X0)) = difference(X0,iPr_def_10(X1)),
inference(demodulation,[status(thm)],[c_224,c_232,c_236,c_239,c_247]) ).
tcf(c_254,plain,
! [X0: $i,X1: $i] : difference(difference(X0,difference(X1,X0)),iPr_def_10(X0)) = difference(X0,difference(X1,X0)),
inference(demodulation,[status(thm)],[c_220,c_236,c_239]) ).
tcf(c_255,plain,
! [X0: $i] : difference(X0,iPr_def_10(X0)) = X0,
inference(demodulation,[status(thm)],[c_254,c_54]) ).
tcf(c_264,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X1),difference(difference(X0,X1),difference(X1,difference(X1,X0)))) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_228,c_229,c_236,c_239]) ).
tcf(c_265,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_264,c_56,c_68]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,difference(X1,difference(X2,X3))),X3) = difference(difference(X0,X3),difference(difference(X1,X2),X3)),
inference(superposition,[status(thm)],[c_96,c_56]) ).
tcf(c_461,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,iPr_def_10(X1))) = difference(iPr_def_10(X1),iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_249,c_55]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),X0) = difference(iPr_def_10(X0),difference(X2,X0)),
inference(superposition,[status(thm)],[c_240,c_56]) ).
tcf(c_490,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,difference(X0,X1))) = difference(difference(X0,X1),iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_240,c_55]) ).
tcf(c_492,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X1) = difference(difference(X0,X1),iPr_def_10(X1)),
inference(superposition,[status(thm)],[c_240,c_56]) ).
tcf(c_517,plain,
! [X0: $i,X1: $i] : difference(iPr_def_10(X0),X1) = iPr_def_10(X0),
inference(superposition,[status(thm)],[c_265,c_64]) ).
tcf(c_619,plain,
! [X0: $i,X1: $i] : difference(X0,iPr_def_10(X1)) = X0,
inference(superposition,[status(thm)],[c_252,c_255]) ).
tcf(c_685,plain,
! [X0: $i,X1: $i,X2: $i] : difference(iPr_def_10(iPr_def_10(X0)),X1) = difference(iPr_def_10(X2),X1),
inference(superposition,[status(thm)],[c_249,c_247]) ).
tcf(c_739,plain,
! [X0: $i,X1: $i,X2: $i] : difference(iPr_def_10(X0),X1) = iPr_def_10(iPr_def_10(X2)),
inference(demodulation,[status(thm)],[c_685,c_517]) ).
tcf(c_765,plain,
! [X0: $i,X1: $i] : difference(X0,X0) = iPr_def_10(X1),
inference(demodulation,[status(thm)],[c_461,c_619,c_517]) ).
tcf(c_789,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),X1) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_492,c_619]) ).
tcf(c_790,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X0,difference(X0,X1))) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_490,c_619]) ).
tcf(c_791,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),X2),X0) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_488,c_517]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,difference(X1,difference(X2,X3))),X3) = difference(difference(X0,difference(X1,X2)),X3),
inference(demodulation,[status(thm)],[c_314,c_56]) ).
tcf(c_856,plain,
! [X0: $i,X1: $i] : difference(X0,difference(iPr_def_10(X1),difference(iPr_def_10(X1),X0))) = X0,
inference(superposition,[status(thm)],[c_619,c_68]) ).
tcf(c_888,plain,
! [X0: $i,X1: $i] : difference(X0,X0) = difference(X1,X1),
inference(superposition,[status(thm)],[c_765,c_765]) ).
tcf(c_897,plain,
! [X0: $i,X1: $i] : difference(difference(X0,X0),X1) = difference(X0,X0),
inference(superposition,[status(thm)],[c_765,c_517]) ).
tcf(c_956,plain,
! [X0: $i,X1: $i,X2: $i] : difference(iPr_def_10(X0),X1) = difference(X2,X2),
inference(superposition,[status(thm)],[c_739,c_765]) ).
tcf(c_1043,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(iPr_def_10(X0),X1),X2) = iPr_def_10(X2),
inference(superposition,[status(thm)],[c_765,c_791]) ).
tcf(c_1062,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(difference(X0,X1),X2))) = difference(difference(difference(X0,X1),X2),iPr_def_10(X0)),
inference(superposition,[status(thm)],[c_791,c_55]) ).
tcf(c_1112,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X0,difference(X1,X2))) = iPr_def_10(difference(X0,difference(X1,X2))),
inference(superposition,[status(thm)],[c_789,c_240]) ).
tcf(c_1130,plain,
! [X0: $i] : difference(X0,X0) = iPr_def_11,
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_888]) ).
tcf(c_1132,plain,
! [X0: $i,X1: $i] : difference(iPr_def_10(X0),X1) = iPr_def_11,
inference(demodulation,[status(thm)],[c_956,c_1130]) ).
tcf(c_1135,plain,
! [X0: $i] : difference(iPr_def_11,X0) = iPr_def_10(X0),
inference(demodulation,[status(thm)],[c_1043,c_1132]) ).
tcf(c_1142,plain,
! [X0: $i] : iPr_def_10(X0) = iPr_def_11,
inference(demodulation,[status(thm)],[c_897,c_1130,c_1135]) ).
tcf(c_1145,plain,
! [X0: $i] : difference(X0,iPr_def_11) = X0,
inference(demodulation,[status(thm)],[c_856,c_1132]) ).
tcf(c_1150,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X0,difference(X1,X2))) = iPr_def_11,
inference(demodulation,[status(thm)],[c_1112,c_1142]) ).
tcf(c_1160,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(difference(X0,X1),X2))) = difference(difference(X0,X1),X2),
inference(demodulation,[status(thm)],[c_1062,c_1142,c_1145]) ).
tcf(c_1784,plain,
! [X0: $i,X1: $i] : difference(X0,difference(X1,difference(X1,X0))) = difference(X0,X1),
inference(superposition,[status(thm)],[c_55,c_790]) ).
tcf(c_2363,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,difference(X1,difference(X2,X0))),difference(X3,difference(X0,X1))) = difference(difference(X0,X1),difference(difference(X2,X0),difference(X3,difference(X0,X1)))),
inference(superposition,[status(thm)],[c_77,c_77]) ).
tcf(c_2364,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(difference(X0,X1),difference(X0,difference(X1,difference(X2,X0))))) = difference(X0,difference(X1,difference(X2,X0))),
inference(superposition,[status(thm)],[c_77,c_790]) ).
tcf(c_2564,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(difference(X1,X2),difference(X1,difference(X2,difference(X0,X1))))) = difference(difference(X0,X1),difference(X1,X2)),
inference(superposition,[status(thm)],[c_77,c_1784]) ).
tcf(c_2617,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X1,X2)) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_2564,c_1145,c_1150]) ).
tcf(c_2620,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X1,difference(X2,X0))) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_2364,c_1145,c_1150]) ).
tcf(c_2626,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,X1),difference(X2,difference(X0,X1))) = difference(difference(X0,X1),difference(X3,X0)),
inference(demodulation,[status(thm)],[c_2363,c_2620]) ).
tcf(c_2627,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X2,X0)) = difference(X0,X1),
inference(demodulation,[status(thm)],[c_2626,c_54]) ).
tcf(c_3458,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(X0,difference(difference(X1,X2),difference(X3,X0))) = difference(X0,difference(X1,difference(X2,difference(X3,X0)))),
inference(superposition,[status(thm)],[c_96,c_2620]) ).
tcf(c_3466,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X2,X1)) = difference(difference(X0,X1),X2),
inference(superposition,[status(thm)],[c_54,c_2620]) ).
tcf(c_3476,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,X1),difference(X2,difference(X3,X0))) = difference(difference(X0,X1),X2),
inference(superposition,[status(thm)],[c_2617,c_2620]) ).
tcf(c_3494,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,X1),difference(X2,difference(X1,difference(X3,X0)))) = difference(difference(X0,X2),difference(X1,difference(X3,X0))),
inference(superposition,[status(thm)],[c_2620,c_56]) ).
tcf(c_3504,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,difference(X1,difference(X2,X3))),difference(X3,X1)) = difference(difference(X0,X3),difference(X1,difference(X2,X3))),
inference(superposition,[status(thm)],[c_2620,c_56]) ).
tcf(c_3590,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,difference(X1,X2)),difference(X2,X3)) = difference(difference(X0,difference(X2,X3)),difference(X1,X2)),
inference(superposition,[status(thm)],[c_2627,c_56]) ).
tcf(c_3594,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,X1),difference(X2,difference(X1,X3))) = difference(difference(X0,X1),X2),
inference(superposition,[status(thm)],[c_2627,c_2620]) ).
tcf(c_3631,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(X0,difference(X1,difference(X2,difference(X3,X0)))) = difference(X0,difference(X1,X2)),
inference(demodulation,[status(thm)],[c_3458,c_2620]) ).
tcf(c_3636,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,difference(X1,X2)),difference(X2,difference(X3,X1))) = difference(difference(X0,X1),difference(X2,difference(X3,X1))),
inference(demodulation,[status(thm)],[c_3504,c_3590]) ).
tcf(c_3637,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),X2) = difference(difference(X0,X2),X1),
inference(demodulation,[status(thm)],[c_3494,c_3476,c_3594]) ).
tcf(c_3900,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(X0,difference(difference(X1,difference(X2,X0)),X3)) = difference(X0,difference(X1,X3)),
inference(superposition,[status(thm)],[c_3637,c_2620]) ).
tcf(c_4964,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,difference(X1,difference(X2,X3))),difference(X3,X1)) = difference(difference(X0,difference(X1,difference(X2,X3))),X3),
inference(superposition,[status(thm)],[c_2620,c_3466]) ).
tcf(c_5345,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(X0,X1),difference(X2,difference(X3,X1))) = difference(difference(X0,difference(X2,X3)),X1),
inference(demodulation,[status(thm)],[c_4964,c_823,c_3590,c_3636]) ).
tcf(c_6675,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(difference(X0,X1),difference(difference(X0,X1),X2)),difference(X1,X2)) = difference(difference(X2,X1),difference(X2,difference(X0,X1))),
inference(superposition,[status(thm)],[c_2620,c_78]) ).
tcf(c_6678,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X0,X1)),difference(X2,X1)) = difference(difference(X1,difference(X2,X1)),difference(X1,X0)),
inference(superposition,[status(thm)],[c_2617,c_78]) ).
tcf(c_6704,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(difference(difference(X0,difference(X1,X2)),difference(difference(X0,difference(X1,X2)),X2)),difference(X3,difference(X2,X0))) = difference(difference(X2,X3),difference(X2,X0)),
inference(superposition,[status(thm)],[c_2620,c_78]) ).
tcf(c_6743,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X1,X2)),difference(difference(X0,difference(X1,X2)),difference(X2,difference(X2,X1)))) = difference(difference(X2,difference(X2,X1)),difference(difference(X1,X0),difference(X1,X2))),
inference(superposition,[status(thm)],[c_78,c_55]) ).
tcf(c_6845,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(difference(X1,difference(X1,X0)),X2))) = difference(difference(X1,difference(X1,X0)),X2),
inference(superposition,[status(thm)],[c_55,c_1160]) ).
tcf(c_6946,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X0,X1)),X2) = difference(X1,difference(X1,difference(X0,X2))),
inference(demodulation,[status(thm)],[c_6845,c_3900]) ).
tcf(c_6951,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X0,X1)),difference(X2,X1)) = difference(X1,difference(X1,X0)),
inference(demodulation,[status(thm)],[c_6678,c_54]) ).
tcf(c_6967,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X0,difference(X2,X1))) = difference(X0,difference(X0,difference(X2,X1))),
inference(demodulation,[status(thm)],[c_6675,c_6951]) ).
tcf(c_6968,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,difference(X0,X1)),X2) = difference(X0,difference(X0,difference(X1,X2))),
inference(demodulation,[status(thm)],[c_6967,c_5345]) ).
tcf(c_6998,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : difference(X0,difference(X0,difference(difference(X1,difference(X2,X0)),difference(X3,difference(X0,X1))))) = difference(difference(X0,X3),difference(X0,X1)),
inference(demodulation,[status(thm)],[c_6704,c_6946,c_6968]) ).
tcf(c_6999,plain,
! [X0: $i,X1: $i,X2: $i] : difference(difference(X0,X1),difference(X0,X2)) = difference(X0,difference(X0,difference(X2,X1))),
inference(demodulation,[status(thm)],[c_6998,c_2620,c_3900]) ).
tcf(c_7031,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(difference(X1,difference(X2,X0)),difference(X0,X2)))) = difference(X0,difference(X0,difference(X2,difference(X2,difference(X2,difference(X0,X1)))))),
inference(demodulation,[status(thm)],[c_6743,c_6946,c_6968,c_6999]) ).
tcf(c_7032,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(X1,difference(X0,X2)))) = difference(X0,difference(X0,difference(X2,difference(X0,X1)))),
inference(demodulation,[status(thm)],[c_7031,c_790,c_3900]) ).
tcf(c_7089,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(X1,difference(X2,difference(X1,X0))))) = difference(difference(X1,X2),difference(X1,X0)),
inference(demodulation,[status(thm)],[c_78,c_6968]) ).
tcf(c_7091,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(X1,difference(X2,difference(X1,X0))))) = difference(X1,difference(X1,difference(X0,X2))),
inference(demodulation,[status(thm)],[c_7089,c_6999]) ).
tcf(c_7092,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X0,difference(X1,X2))) = difference(X1,difference(X1,difference(X0,X2))),
inference(demodulation,[status(thm)],[c_7091,c_3631]) ).
tcf(c_7093,plain,
difference(a,difference(a,difference(b,difference(b,c)))) != difference(a,difference(a,difference(c,difference(a,b)))),
inference(demodulation,[status(thm)],[c_66,c_7092]) ).
tcf(c_7094,plain,
difference(a,difference(a,difference(b,difference(a,c)))) != difference(a,difference(a,difference(b,difference(b,c)))),
inference(demodulation,[status(thm)],[c_7093,c_7032]) ).
tcf(c_8077,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X1,difference(X0,difference(X0,X2)))) = difference(X0,difference(X1,X2)),
inference(superposition,[status(thm)],[c_55,c_3631]) ).
tcf(c_12264,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X1,difference(X1,difference(X0,X2)))) = difference(X0,difference(X1,X2)),
inference(superposition,[status(thm)],[c_6968,c_3900]) ).
tcf(c_14610,plain,
! [X0: $i,X1: $i,X2: $i] : difference(X0,difference(X1,difference(X0,X2))) = difference(X0,difference(X1,difference(X1,X2))),
inference(superposition,[status(thm)],[c_12264,c_8077]) ).
tcf(c_14989,plain,
difference(a,difference(a,difference(b,difference(a,c)))) != difference(a,difference(a,difference(b,difference(a,c)))),
inference(demodulation,[status(thm)],[c_7094,c_14610]) ).
tcf(c_14990,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_14989]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG005-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.62 % Computer : n019.cluster.edu
% 0.14/10.62 % Model : x86_64 x86_64
% 0.14/10.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.62 % Memory : 8046.5625MB
% 0.14/10.62 % OS : Linux 6.8.0-71-generic
% 0.14/10.62 % CPULimit : 300
% 0.14/10.62 % WCLimit : 300
% 0.14/10.62 % DateTime : Fri Sep 25 04:30:45 UTC 2026
% 0.14/10.62 % CPUTime :
% 0.14/10.62 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/10.65 Running UEQ theorem proving
% 0.14/10.65 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s ueq_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/10.66
% 0.14/10.66 % ======== iProver multi-core TPTP/SMT =========
% 0.14/10.66
% 0.14/10.66 % Detected problem language: tptp
% 0.14/10.68 % Proving...
% 9.25/12.44 WARNING - Clausifier option not provided in the heuristic config "heur/vip2_118404", setting default options.
% 9.25/12.44 % SZS status Started for theBenchmark.p
% 9.25/12.44 % SZS status Unsatisfiable for theBenchmark.p
% 9.25/12.44
% 9.25/12.44 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 9.25/12.44
% 9.25/12.44 % ------ iProver source info
% 9.25/12.44
% 9.25/12.44 % git: date: 2026-07-19 20:42:38 +0200
% 9.25/12.44 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 9.25/12.44 % git: non_committed_changes: false
% 9.25/12.44
% 9.25/12.44 % ------ Parsing...% successful
% 9.25/12.44
% 9.25/12.44
% 9.25/12.44 % ------ Clausification by vclausify_rel & Parsing by iProver...
% 9.25/12.44 % ------ Proving...
% 9.25/12.44 % ------ Problem Properties
% 9.25/12.44
% 9.25/12.44 %
% 9.25/12.44 % clauses 4
% 9.25/12.44 % conjectures 1
% 9.25/12.44 % EPR 0
% 9.25/12.44 % Horn 4
% 9.25/12.44 % unary 4
% 9.25/12.44 % binary 0
% 9.25/12.44 % lits 4
% 9.25/12.44 % lits eq 4
% 9.25/12.44 % fd_pure 0
% 9.25/12.44 % fd_pseudo 0
% 9.25/12.44 % fd_cond 0
% 9.25/12.44 % fd_pseudo_cond 0
% 9.25/12.44 % AC symbols 0
% 9.25/12.44
% 9.25/12.44 % ------ Input Options Time Limit: Unbounded
% 9.25/12.44
% 9.25/12.44
% 9.25/12.44 % ------
% 9.25/12.44 % Current options:
% 9.25/12.44 % ------
% 9.25/12.44
% 9.25/12.44
% 9.25/12.44 %
% 9.25/12.44
% 9.25/12.44 % ------ Proving...
% 9.25/12.44 %
% 9.25/12.44
% 9.25/12.44 % SZS status Unsatisfiable for theBenchmark.p
% 9.25/12.44
% 9.25/12.44 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 9.25/12.44
% 9.25/12.44
%------------------------------------------------------------------------------