%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP667-10 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.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 : Tue May 5 04:26:49 PM UTC 2026
% Result : Unsatisfiable 34.89s 20.60s
% Output : CNFRefutation 34.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 4 RR)
% Number of literals : 70 ( 69 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 138 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(f08,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
cnf(f03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(f04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(f01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(f05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(f06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
cnf(f07,axiom,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
cnf(f12,axiom,
ifeq(mult(mult(X1,X2),mult(X3,X1)),mult(X1,mult(mult(X2,X3),X1)),mult(X1,mult(X2,mult(X1,X3))),mult(mult(mult(X1,X2),X1),X3)) = mult(mult(mult(X1,X2),X1),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f12) ).
cnf(f10,axiom,
ifeq(mult(X1,mult(X2,mult(X3,X2))),mult(mult(mult(X1,X2),X3),X2),mult(X2,mult(X1,mult(X2,X3))),mult(mult(mult(X2,X1),X2),X3)) = mult(mult(mult(X2,X1),X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
cnf(ifeq_axiom,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(f09,axiom,
mult(f(X1),f(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
cnf(goals,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_13,axiom,
ld(X1,mult(X1,X2)) = X2,
f02 ).
cnf(c_0_14,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
f08 ).
cnf(c_0_15,plain,
ld(mult(X1,X2),mult(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,axiom,
mult(rd(X1,X2),X2) = X1,
f03 ).
cnf(c_0_17,axiom,
rd(mult(X1,X2),X2) = X1,
f04 ).
cnf(c_0_18,axiom,
mult(X1,ld(X1,X2)) = X2,
f01 ).
cnf(c_0_19,plain,
ld(mult(X1,rd(X2,X1)),mult(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,axiom,
mult(X1,unit) = X1,
f05 ).
cnf(c_0_21,axiom,
mult(unit,X1) = X1,
f06 ).
cnf(c_0_22,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
ld(mult(X1,rd(unit,X1)),X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_17,c_0_21]) ).
cnf(c_0_25,axiom,
mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
f07 ).
cnf(c_0_26,plain,
mult(X1,rd(unit,X1)) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_14]),c_0_14]) ).
cnf(c_0_28,plain,
rd(unit,X1) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_29,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_30,axiom,
ifeq(mult(mult(X1,X2),mult(X3,X1)),mult(X1,mult(mult(X2,X3),X1)),mult(X1,mult(X2,mult(X1,X3))),mult(mult(mult(X1,X2),X1),X3)) = mult(mult(mult(X1,X2),X1),X3),
f12 ).
cnf(c_0_31,plain,
rd(mult(mult(X1,X2),mult(X3,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X3,X2))),
inference(spm,[status(thm)],[c_0_17,c_0_27]) ).
cnf(c_0_32,plain,
mult(ld(X1,unit),X1) = unit,
inference(spm,[status(thm)],[c_0_16,c_0_28]) ).
cnf(c_0_33,plain,
rd(mult(X1,X2),X1) = mult(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_29,c_0_16]) ).
cnf(c_0_34,axiom,
ifeq(mult(X1,mult(X2,mult(X3,X2))),mult(mult(mult(X1,X2),X3),X2),mult(X2,mult(X1,mult(X2,X3))),mult(mult(mult(X2,X1),X2),X3)) = mult(mult(mult(X2,X1),X2),X3),
f10 ).
cnf(c_0_35,plain,
mult(mult(X1,mult(X2,X1)),X2) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_21]),c_0_21]) ).
cnf(c_0_36,plain,
ifeq(mult(mult(X1,X2),mult(X3,X1)),mult(X1,mult(mult(X2,X3),X1)),mult(X1,mult(X2,mult(X1,X3))),mult(mult(X1,mult(X2,X1)),X3)) = mult(mult(X1,mult(X2,X1)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_14]),c_0_14]) ).
cnf(c_0_37,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_38,plain,
mult(ld(X1,unit),mult(X1,mult(X2,X1))) = mult(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_21]),c_0_33]),c_0_17]) ).
cnf(c_0_39,plain,
ifeq(mult(X1,mult(X2,mult(X3,X2))),mult(mult(mult(X1,X2),X3),X2),mult(X2,mult(X1,mult(X2,X3))),mult(mult(X2,mult(X1,X2)),X3)) = mult(mult(X2,mult(X1,X2)),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_14]),c_0_14]) ).
cnf(c_0_40,plain,
mult(mult(X1,X2),mult(X1,mult(X2,X1))) = mult(X1,mult(X2,mult(X1,mult(X2,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_27]),c_0_35]) ).
cnf(c_0_41,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_21]),c_0_20]),c_0_21]),c_0_21]),c_0_37]) ).
cnf(c_0_42,plain,
mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_43,plain,
mult(ld(X1,unit),mult(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_38,c_0_16]) ).
cnf(c_0_44,plain,
mult(X1,mult(mult(X1,X2),mult(X1,X2))) = mult(X1,mult(X1,mult(X2,mult(X1,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_14]),c_0_35]),c_0_27]),c_0_40]),c_0_14]),c_0_27]),c_0_41]),c_0_37]),c_0_14]),c_0_27]),c_0_41]) ).
cnf(c_0_45,plain,
ld(X1,mult(X2,X1)) = mult(ld(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_42]) ).
cnf(c_0_46,plain,
ld(ld(X1,unit),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_43]) ).
cnf(c_0_47,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_44]),c_0_13]) ).
cnf(c_0_48,plain,
mult(mult(X1,X2),ld(X1,unit)) = mult(X1,mult(X2,ld(X1,unit))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_46]) ).
cnf(c_0_49,plain,
mult(ld(X1,unit),X2) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_43,c_0_18]) ).
cnf(c_0_50,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_20]),c_0_21]),c_0_21]) ).
cnf(c_0_51,plain,
mult(rd(X1,X2),mult(X2,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_47,c_0_16]) ).
cnf(c_0_52,plain,
mult(mult(X1,ld(X2,unit)),mult(X2,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_48]),c_0_49]),c_0_13]),c_0_49]),c_0_13]),c_0_50]),c_0_43]) ).
cnf(c_0_53,plain,
rd(mult(X1,X1),mult(X2,X1)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_17,c_0_51]) ).
cnf(c_0_54,plain,
mult(X1,ld(X2,unit)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_52]),c_0_53]) ).
cnf(c_0_55,plain,
mult(X1,mult(ld(X1,X2),X2)) = mult(X2,X2),
inference(spm,[status(thm)],[c_0_47,c_0_18]) ).
cnf(c_0_56,axiom,
mult(f(X1),f(X1)) = X1,
f09 ).
cnf(c_0_57,plain,
ld(X1,rd(X1,X2)) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_13,c_0_54]) ).
cnf(c_0_58,plain,
ld(X1,mult(X2,X2)) = mult(ld(X1,X2),X2),
inference(spm,[status(thm)],[c_0_13,c_0_55]) ).
cnf(c_0_59,plain,
mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(mult(X1,X3),mult(ld(X3,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_42]),c_0_18]) ).
cnf(c_0_60,plain,
mult(f(X1),mult(f(X1),X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_56]) ).
cnf(c_0_61,plain,
ld(mult(X1,X2),X1) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_57,c_0_17]) ).
cnf(c_0_62,plain,
mult(ld(X1,f(X2)),f(X2)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_58,c_0_56]) ).
cnf(c_0_63,plain,
rd(mult(X1,mult(X2,X3)),X3) = mult(mult(X1,X3),ld(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_60]),c_0_61]),c_0_54]),c_0_61]),c_0_49]),c_0_59]),c_0_62]) ).
cnf(c_0_64,plain,
mult(mult(mult(X1,X2),ld(X2,X3)),X2) = mult(X1,mult(X3,X2)),
inference(spm,[status(thm)],[c_0_16,c_0_63]) ).
cnf(c_0_65,negated_conjecture,
mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
goals ).
cnf(c_0_66,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_13]),c_0_14]) ).
cnf(c_0_67,negated_conjecture,
mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
inference(rw,[status(thm)],[c_0_65,c_0_14]) ).
cnf(c_0_68,plain,
mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_66]),c_0_37]) ).
cnf(c_0_69,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP667-10 : TPTP v9.2.1. Released v7.5.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.32 % Computer : n023.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 19:01:38 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 34.89/20.60 % Version : CSE_E---1.7
% 34.89/20.60 % Problem : theBenchmark.p
% 34.89/20.60 % SZS status Unsatisfiable for theBenchmark.p
% 34.89/20.60 % SZS output start CNFRefutation
% See solution above
% 34.98/20.73 % Total time : 15.395s
%------------------------------------------------------------------------------