%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP696-1 : TPTP v9.2.1. Released v4.0.0.
% 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 : n028.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 04:27:05 PM UTC 2026
% Result : Unsatisfiable 68.62s 39.47s
% Output : CNFRefutation 68.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 12
% Syntax : Number of clauses : 79 ( 79 unt; 0 nHn; 3 RR)
% Number of literals : 79 ( 78 equ; 2 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02) ).
cnf(c11,axiom,
mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11) ).
cnf(c04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c04) ).
cnf(c10,axiom,
mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10) ).
cnf(c03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03) ).
cnf(c07,axiom,
mult(X1,i(mult(X2,X1))) = i(X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
cnf(c01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01) ).
cnf(c08,axiom,
mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c08) ).
cnf(c05,axiom,
mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c05) ).
cnf(c09,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
cnf(c06,axiom,
mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
cnf(goals,negated_conjecture,
mult(mult(mult(a,b),a),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_12,axiom,
ld(X1,mult(X1,X2)) = X2,
c02 ).
cnf(c_0_13,axiom,
mult(X1,i(X1)) = unit,
c11 ).
cnf(c_0_14,axiom,
rd(mult(X1,X2),X2) = X1,
c04 ).
cnf(c_0_15,axiom,
mult(i(X1),X1) = unit,
c10 ).
cnf(c_0_16,plain,
ld(X1,unit) = i(X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
i(X1) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,axiom,
mult(rd(X1,X2),X2) = X1,
c03 ).
cnf(c_0_19,axiom,
mult(X1,i(mult(X2,X1))) = i(X2),
c07 ).
cnf(c_0_20,plain,
ld(X1,unit) = rd(unit,X1),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_21,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_18]) ).
cnf(c_0_22,plain,
mult(X1,rd(unit,mult(X2,X1))) = rd(unit,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_17]),c_0_17]) ).
cnf(c_0_23,axiom,
mult(X1,ld(X1,X2)) = X2,
c01 ).
cnf(c_0_24,axiom,
mult(X1,mult(X2,X3)) = mult(rd(mult(X1,X2),X1),mult(X1,X3)),
c08 ).
cnf(c_0_25,plain,
mult(X1,rd(unit,X1)) = unit,
inference(rw,[status(thm)],[c_0_13,c_0_17]) ).
cnf(c_0_26,axiom,
mult(X1,unit) = X1,
c05 ).
cnf(c_0_27,plain,
rd(unit,rd(unit,X1)) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_28,plain,
ld(X1,rd(unit,X2)) = rd(unit,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_29,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_14,c_0_23]) ).
cnf(c_0_30,plain,
rd(unit,rd(X1,X2)) = mult(X2,rd(unit,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_18]) ).
cnf(c_0_31,plain,
mult(X1,mult(X2,rd(unit,X1))) = rd(mult(X1,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_32,plain,
mult(rd(unit,mult(X1,X2)),X1) = rd(unit,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_22]),c_0_27]) ).
cnf(c_0_33,plain,
rd(unit,mult(rd(unit,X1),X2)) = ld(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_20]) ).
cnf(c_0_34,plain,
rd(unit,mult(X1,rd(unit,X2))) = rd(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_30]),c_0_20]) ).
cnf(c_0_35,plain,
ld(X1,rd(mult(X1,X2),X1)) = mult(X2,rd(unit,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_31]) ).
cnf(c_0_36,plain,
mult(rd(unit,X1),rd(X1,X2)) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_32,c_0_18]) ).
cnf(c_0_37,plain,
rd(rd(unit,X1),X2) = rd(unit,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_14,c_0_32]) ).
cnf(c_0_38,plain,
ld(rd(unit,X1),X2) = rd(X1,rd(unit,X2)),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_39,plain,
rd(unit,ld(X1,X2)) = mult(rd(unit,X2),X1),
inference(spm,[status(thm)],[c_0_32,c_0_23]) ).
cnf(c_0_40,plain,
rd(X1,unit) = X1,
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_41,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),ld(X3,mult(X2,X3))),
c09 ).
cnf(c_0_42,axiom,
mult(unit,X1) = X1,
c06 ).
cnf(c_0_43,plain,
rd(X1,mult(rd(unit,X1),X2)) = mult(rd(X1,X2),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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_33]),c_0_38]),c_0_39]),c_0_30]),c_0_40]),c_0_26]) ).
cnf(c_0_44,plain,
rd(X1,rd(X1,X2)) = mult(mult(X1,X2),rd(unit,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_25]),c_0_38]),c_0_34]),c_0_42]) ).
cnf(c_0_45,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_14,c_0_42]) ).
cnf(c_0_46,plain,
rd(X1,rd(X2,rd(unit,X1))) = rd(unit,X2),
inference(spm,[status(thm)],[c_0_34,c_0_18]) ).
cnf(c_0_47,plain,
rd(mult(X1,X2),rd(unit,X2)) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_32]),c_0_24]) ).
cnf(c_0_48,plain,
mult(ld(X1,X2),rd(unit,X2)) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_49,plain,
mult(mult(X1,X1),rd(unit,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_40]) ).
cnf(c_0_50,plain,
rd(X1,mult(X2,mult(X1,X1))) = rd(unit,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
mult(ld(X1,rd(X2,X3)),mult(X3,rd(unit,X2))) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_48,c_0_30]) ).
cnf(c_0_52,plain,
rd(X1,rd(unit,X1)) = mult(X1,X1),
inference(spm,[status(thm)],[c_0_14,c_0_49]) ).
cnf(c_0_53,plain,
rd(unit,mult(ld(X1,X2),X3)) = ld(X3,mult(rd(unit,X2),X1)),
inference(spm,[status(thm)],[c_0_28,c_0_39]) ).
cnf(c_0_54,plain,
mult(rd(X1,mult(X2,X1)),X1) = ld(X2,X1),
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_43,c_0_31]),c_0_46]),c_0_33]),c_0_30]),c_0_40]),c_0_26]) ).
cnf(c_0_55,plain,
rd(mult(X1,ld(X2,X1)),X1) = mult(X1,rd(unit,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]) ).
cnf(c_0_56,plain,
rd(X1,ld(X2,mult(X1,X1))) = ld(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(spm,[status(thm)],[c_0_50,c_0_51]),c_0_37]),c_0_33]),c_0_52]),c_0_53]),c_0_38]),c_0_33]) ).
cnf(c_0_57,plain,
rd(ld(X1,X2),X2) = rd(X2,mult(X1,X2)),
inference(spm,[status(thm)],[c_0_14,c_0_54]) ).
cnf(c_0_58,plain,
rd(X1,mult(X1,mult(X2,X1))) = rd(unit,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_24]),c_0_18]) ).
cnf(c_0_59,plain,
mult(ld(X1,X2),rd(unit,X1)) = ld(X1,rd(X2,X1)),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_60,plain,
mult(mult(rd(unit,X1),X2),X1) = ld(X1,mult(X2,X1)),
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_37,c_0_44]),c_0_30]),c_0_40]),c_0_26]),c_0_37]),c_0_33]) ).
cnf(c_0_61,plain,
mult(mult(X1,rd(unit,X2)),X1) = mult(X1,ld(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_55]) ).
cnf(c_0_62,plain,
ld(ld(X1,X2),X1) = ld(X2,mult(X1,X1)),
inference(spm,[status(thm)],[c_0_21,c_0_56]) ).
cnf(c_0_63,plain,
rd(X1,mult(rd(X1,X2),X1)) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_57,c_0_21]) ).
cnf(c_0_64,plain,
mult(ld(X1,X2),X2) = ld(X1,mult(X2,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(spm,[status(thm)],[c_0_58,c_0_59]),c_0_37]),c_0_60]),c_0_39]),c_0_53]),c_0_30]),c_0_61]),c_0_12]),c_0_33]),c_0_62]) ).
cnf(c_0_65,plain,
rd(ld(X1,mult(X2,X2)),X2) = rd(X2,mult(ld(X2,X1),X2)),
inference(spm,[status(thm)],[c_0_63,c_0_56]) ).
cnf(c_0_66,plain,
rd(X1,mult(ld(X1,X2),X1)) = ld(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_64]),c_0_65]) ).
cnf(c_0_67,plain,
ld(X1,mult(rd(X1,X2),X1)) = mult(rd(unit,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_22]),c_0_34]) ).
cnf(c_0_68,plain,
mult(rd(unit,X1),ld(X2,X1)) = ld(mult(X2,X1),X1),
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_33,c_0_31]),c_0_30]),c_0_33]),c_0_30]),c_0_40]),c_0_26]) ).
cnf(c_0_69,plain,
ld(mult(X1,X2),X1) = rd(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_66,c_0_12]) ).
cnf(c_0_70,plain,
mult(X1,mult(rd(unit,X2),X1)) = mult(rd(X1,X2),X1),
inference(spm,[status(thm)],[c_0_23,c_0_67]) ).
cnf(c_0_71,plain,
ld(mult(mult(X1,X2),X1),X1) = rd(unit,mult(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_36]) ).
cnf(c_0_72,plain,
mult(rd(X1,rd(unit,X2)),X1) = mult(X1,mult(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_63]),c_0_40]),c_0_26]) ).
cnf(c_0_73,plain,
rd(X1,rd(unit,mult(X2,X1))) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_29,c_0_71]) ).
cnf(c_0_74,plain,
mult(mult(mult(X1,X2),X1),X1) = mult(X1,mult(mult(X2,X1),X1)),
inference(spm,[status(thm)],[c_0_72,c_0_73]) ).
cnf(c_0_75,plain,
rd(mult(X1,mult(mult(X2,X1),X1)),X1) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_14,c_0_74]) ).
cnf(c_0_76,negated_conjecture,
mult(mult(mult(a,b),a),mult(a,c)) != mult(a,mult(mult(mult(b,a),a),c)),
goals ).
cnf(c_0_77,plain,
mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
inference(spm,[status(thm)],[c_0_24,c_0_75]) ).
cnf(c_0_78,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_76,c_0_77])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP696-1 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 19:02:30 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 68.62/39.47 % Version : CSE_E---1.7
% 68.62/39.47 % Problem : theBenchmark.p
% 68.62/39.47 % SZS status Unsatisfiable for theBenchmark.p
% 68.62/39.47 % SZS output start CNFRefutation
% See solution above
% 68.92/39.72 % Total time : 30.433s
%------------------------------------------------------------------------------