%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP684-1 : 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 : n014.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 04:26:53 PM UTC 2026
% Result : Unsatisfiable 1.98s 1.94s
% Output : CNFRefutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 8
% Syntax : Number of clauses : 78 ( 78 unt; 0 nHn; 5 RR)
% Number of literals : 78 ( 77 equ; 4 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 166 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c02,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
cnf(c04,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
cnf(c01,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c01) ).
cnf(c03,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
cnf(c07,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
cnf(c06,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c06) ).
cnf(c05,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c05) ).
cnf(goals,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_8,axiom,
rd(mult(X1,X1),X1) = X1,
c02 ).
cnf(c_0_9,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
c04 ).
cnf(c_0_10,axiom,
ld(X1,mult(X1,X1)) = X1,
c01 ).
cnf(c_0_11,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
c03 ).
cnf(c_0_12,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
c07 ).
cnf(c_0_13,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_15,plain,
mult(X1,ld(X1,ld(X2,X2))) = mult(rd(rd(X1,X1),X2),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_9]) ).
cnf(c_0_16,plain,
mult(rd(rd(X1,X1),X1),X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_17,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
c06 ).
cnf(c_0_18,plain,
ld(X1,X1) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_14]),c_0_15]),c_0_16]) ).
cnf(c_0_19,plain,
mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_9]),c_0_9]) ).
cnf(c_0_20,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_14,c_0_18]) ).
cnf(c_0_21,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(X1,mult(rd(ld(X1,X1),X3),X3)),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_22,plain,
mult(rd(X1,rd(X1,X1)),rd(X1,X1)) = rd(X1,rd(X1,X1)),
inference(spm,[status(thm)],[c_0_9,c_0_20]) ).
cnf(c_0_23,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(X1,mult(rd(rd(X1,X1),X3),X3)),
inference(rw,[status(thm)],[c_0_21,c_0_18]) ).
cnf(c_0_24,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
c05 ).
cnf(c_0_25,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(rd(X1,X1),mult(rd(X1,X3),X3)),
inference(spm,[status(thm)],[c_0_19,c_0_13]) ).
cnf(c_0_26,plain,
mult(X1,ld(X1,rd(X2,X2))) = mult(rd(rd(X1,X1),X2),X2),
inference(rw,[status(thm)],[c_0_15,c_0_18]) ).
cnf(c_0_27,plain,
rd(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22,c_0_23]),c_0_16]),c_0_20]) ).
cnf(c_0_28,plain,
mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_11]),c_0_11]) ).
cnf(c_0_29,plain,
mult(rd(X1,X1),mult(rd(X1,X2),X2)) = mult(X1,mult(rd(rd(X1,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_30,plain,
mult(rd(rd(rd(X1,X1),rd(X1,X1)),X1),X1) = rd(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_18]),c_0_20]) ).
cnf(c_0_31,plain,
mult(rd(X1,rd(X2,X1)),rd(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_16]),c_0_20]) ).
cnf(c_0_32,plain,
mult(X1,mult(rd(X2,rd(X3,X3)),rd(X3,X3))) = mult(rd(mult(X1,X2),X3),X3),
inference(spm,[status(thm)],[c_0_19,c_0_27]) ).
cnf(c_0_33,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(rd(rd(X1,X1),X3),X3),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_13]),c_0_26]) ).
cnf(c_0_34,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_13]),c_0_30]) ).
cnf(c_0_35,plain,
mult(rd(X1,mult(rd(X2,X1),X1)),mult(rd(X2,X1),X1)) = X1,
inference(spm,[status(thm)],[c_0_31,c_0_9]) ).
cnf(c_0_36,plain,
mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_27]),c_0_20]),c_0_9]) ).
cnf(c_0_37,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_16]),c_0_13]) ).
cnf(c_0_38,plain,
mult(rd(X1,X1),ld(rd(X1,X1),X1)) = ld(rd(X1,X1),X1),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_39,plain,
rd(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_34]),c_0_18]),c_0_18]),c_0_20]) ).
cnf(c_0_40,plain,
mult(rd(X1,mult(X2,X1)),mult(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_9]),c_0_36]),c_0_36]) ).
cnf(c_0_41,plain,
mult(ld(X1,X2),mult(ld(X1,X2),ld(ld(X1,X2),X3))) = mult(mult(X1,ld(X1,ld(X1,X2))),X3),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_42,plain,
ld(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_18]),c_0_38]) ).
cnf(c_0_43,plain,
mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_32]),c_0_19]) ).
cnf(c_0_44,plain,
mult(rd(rd(X1,X2),X2),X2) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_31]) ).
cnf(c_0_45,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_42]),c_0_13]) ).
cnf(c_0_46,plain,
rd(mult(X1,mult(rd(X2,X3),X3)),X3) = rd(mult(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_43]),c_0_44]) ).
cnf(c_0_47,plain,
mult(X1,mult(rd(rd(X1,X1),X2),X2)) = mult(X1,rd(X2,X2)),
inference(spm,[status(thm)],[c_0_45,c_0_26]) ).
cnf(c_0_48,plain,
rd(mult(X1,rd(X2,X2)),X2) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_20]) ).
cnf(c_0_49,plain,
mult(rd(X1,X2),X2) = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_48]),c_0_44]) ).
cnf(c_0_50,plain,
mult(rd(X1,X2),rd(X2,X2)) = rd(X1,X2),
inference(rw,[status(thm)],[c_0_44,c_0_49]) ).
cnf(c_0_51,plain,
mult(mult(X1,ld(X1,X2)),ld(mult(X1,ld(X1,X2)),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_52,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(rd(X1,X1),X3),
inference(rw,[status(thm)],[c_0_33,c_0_36]) ).
cnf(c_0_53,plain,
rd(X1,rd(X2,X2)) = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_39]),c_0_49]),c_0_39]) ).
cnf(c_0_54,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_18]),c_0_20]),c_0_20]) ).
cnf(c_0_55,plain,
mult(X1,ld(X1,X2)) = mult(rd(X1,X1),X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_42]),c_0_53]),c_0_50]) ).
cnf(c_0_56,plain,
rd(mult(X1,X2),X2) = mult(X1,rd(X2,X2)),
inference(rw,[status(thm)],[c_0_9,c_0_49]) ).
cnf(c_0_57,plain,
mult(mult(rd(X1,X1),X2),X3) = mult(rd(X1,X1),mult(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_55]) ).
cnf(c_0_58,plain,
mult(mult(X1,X2),rd(X3,X3)) = mult(X1,mult(X2,rd(X3,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_49]),c_0_49]) ).
cnf(c_0_59,plain,
rd(mult(rd(X1,X1),mult(X2,X3)),X3) = mult(rd(X1,X1),mult(X2,rd(X3,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]) ).
cnf(c_0_60,plain,
rd(mult(X1,mult(X2,rd(X3,X3))),X3) = rd(mult(X1,X2),X3),
inference(rw,[status(thm)],[c_0_46,c_0_49]) ).
cnf(c_0_61,plain,
rd(mult(rd(X1,X1),X2),X3) = mult(rd(X1,X1),rd(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_49]),c_0_60]),c_0_50]) ).
cnf(c_0_62,plain,
mult(rd(X1,X1),rd(X1,X2)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_49]),c_0_20]) ).
cnf(c_0_63,plain,
mult(X1,rd(rd(X2,X3),rd(X2,X3))) = mult(X1,rd(X3,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_47]),c_0_49]) ).
cnf(c_0_64,plain,
mult(rd(X1,rd(X2,rd(X1,X1))),rd(X2,rd(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_13]),c_0_20]) ).
cnf(c_0_65,plain,
rd(rd(X1,X2),rd(X1,X2)) = mult(rd(X1,X1),rd(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_62]),c_0_63]) ).
cnf(c_0_66,plain,
mult(X1,rd(mult(X2,rd(X1,X1)),mult(X2,rd(X1,X1)))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_49]),c_0_53]),c_0_53]) ).
cnf(c_0_67,negated_conjecture,
rd(mult(a,mult(b,c)),mult(b,c)) != rd(mult(a,c),c),
goals ).
cnf(c_0_68,plain,
mult(rd(X1,X2),mult(X2,rd(X3,X3))) = mult(X1,mult(rd(X2,X2),rd(X3,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_49]),c_0_58]) ).
cnf(c_0_69,plain,
mult(X1,mult(rd(X2,X2),rd(X3,X3))) = mult(X1,rd(X3,X3)),
inference(rw,[status(thm)],[c_0_63,c_0_65]) ).
cnf(c_0_70,plain,
mult(rd(X1,X2),rd(mult(X3,rd(X2,X2)),mult(X3,rd(X2,X2)))) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_66,c_0_63]) ).
cnf(c_0_71,plain,
mult(X1,rd(mult(X2,X1),mult(X2,X1))) = X1,
inference(rw,[status(thm)],[c_0_40,c_0_49]) ).
cnf(c_0_72,negated_conjecture,
mult(rd(a,mult(b,c)),mult(b,c)) != mult(rd(a,c),c),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_67,c_0_9]),c_0_9]) ).
cnf(c_0_73,plain,
mult(rd(X1,X2),mult(X2,rd(X3,X3))) = mult(X1,rd(X3,X3)),
inference(rw,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,plain,
mult(rd(X1,mult(X2,X3)),rd(X3,X3)) = rd(X1,mult(X2,X3)),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,negated_conjecture,
mult(a,rd(mult(b,c),mult(b,c))) != mult(a,rd(c,c)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_49]),c_0_49]) ).
cnf(c_0_76,plain,
mult(X1,rd(mult(X2,X3),mult(X2,X3))) = mult(X1,rd(X3,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_49]),c_0_63]) ).
cnf(c_0_77,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_75,c_0_76])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP684-1 : 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
% 0.16/0.34 % Computer : n014.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 19:02:21 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.98/1.94 % Version : CSE_E---1.7
% 1.98/1.94 % Problem : theBenchmark.p
% 1.98/1.94 % SZS status Unsatisfiable for theBenchmark.p
% 1.98/1.94 % SZS output start CNFRefutation
% See solution above
% 1.98/1.94 % Total time : 1.374s
%------------------------------------------------------------------------------