%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP668-1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n025.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 04:26:51 PM UTC 2026
% Result : Unsatisfiable 4.15s 3.25s
% Output : CNFRefutation 4.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of clauses : 51 ( 51 unt; 0 nHn; 5 RR)
% Number of literals : 51 ( 50 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c08,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(c07,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(goals,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_9,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_10,axiom,
mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
c08 ).
cnf(c_0_11,plain,
rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_13,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_14,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_15,axiom,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
c07 ).
cnf(c_0_16,plain,
rd(mult(X1,X2),X1) = mult(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_17,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_18,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
cnf(c_0_19,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_20,plain,
mult(X1,rd(unit,X1)) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_14]),c_0_17]) ).
cnf(c_0_21,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_22,plain,
mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_12]) ).
cnf(c_0_23,plain,
rd(unit,X1) = ld(X1,unit),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
mult(rd(X1,X2),mult(X2,mult(X2,X3))) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,plain,
mult(ld(X1,unit),X1) = unit,
inference(spm,[status(thm)],[c_0_12,c_0_23]) ).
cnf(c_0_26,plain,
mult(mult(X1,ld(X2,unit)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_14]),c_0_12]) ).
cnf(c_0_27,plain,
rd(X1,ld(X2,unit)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_28,plain,
rd(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_21]) ).
cnf(c_0_29,plain,
mult(X1,ld(X2,unit)) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_26]) ).
cnf(c_0_30,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_31,plain,
mult(mult(X1,mult(X2,rd(X2,X3))),X3) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]) ).
cnf(c_0_32,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_30]) ).
cnf(c_0_33,plain,
mult(ld(X1,unit),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_23]),c_0_13]) ).
cnf(c_0_34,plain,
mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
mult(mult(X1,X2),mult(X2,X2)) = mult(X1,mult(X2,mult(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_18]),c_0_21]) ).
cnf(c_0_36,plain,
mult(ld(X1,unit),mult(X1,X2)) = X2,
inference(spm,[status(thm)],[c_0_33,c_0_30]) ).
cnf(c_0_37,plain,
mult(mult(X1,X2),ld(X2,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_13]),c_0_13]) ).
cnf(c_0_38,plain,
mult(mult(X1,X2),mult(X2,mult(X2,X2))) = mult(X1,mult(X2,mult(X2,mult(X2,X2)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_18]),c_0_21]) ).
cnf(c_0_39,plain,
mult(mult(X1,mult(X2,mult(X2,mult(X3,X3)))),X4) = mult(X1,mult(X2,mult(X2,mult(X3,mult(X3,X4))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_21]),c_0_21]) ).
cnf(c_0_40,plain,
mult(X1,mult(X2,mult(X2,ld(mult(X1,mult(X2,X2)),X3)))) = X3,
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_41,plain,
ld(ld(X1,unit),X2) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_42,negated_conjecture,
mult(mult(a,b),mult(mult(c,b),c)) != mult(mult(a,mult(mult(b,c),b)),c),
goals ).
cnf(c_0_43,plain,
mult(mult(X1,X2),mult(X1,X2)) = mult(X1,mult(X2,mult(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]),c_0_40]) ).
cnf(c_0_44,plain,
rd(X1,mult(X2,X1)) = ld(X2,unit),
inference(spm,[status(thm)],[c_0_32,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
mult(mult(a,mult(b,mult(c,b))),c) != mult(mult(a,b),mult(c,mult(b,c))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_10]),c_0_10]) ).
cnf(c_0_46,plain,
mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_9]),c_0_10]),c_0_43]) ).
cnf(c_0_47,plain,
mult(mult(X1,rd(X2,X3)),mult(X3,X2)) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_44]),c_0_29]) ).
cnf(c_0_48,negated_conjecture,
mult(mult(a,b),mult(c,mult(b,c))) != mult(a,mult(b,mult(c,mult(b,c)))),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,plain,
mult(mult(X1,X2),mult(X3,mult(X2,X3))) = mult(X1,mult(X2,mult(X3,mult(X2,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_9]),c_0_43]) ).
cnf(c_0_50,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP668-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.17/0.34 % Computer : n025.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 19:00:58 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 4.15/3.25 % Version : CSE_E---1.7
% 4.15/3.25 % Problem : theBenchmark.p
% 4.15/3.25 % SZS status Unsatisfiable for theBenchmark.p
% 4.15/3.25 % SZS output start CNFRefutation
% See solution above
% 4.15/3.26 % Total time : 2.375s
%------------------------------------------------------------------------------