%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP754-1 : 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 : n009.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 04:27:13 PM UTC 2026
% Result : Unsatisfiable 33.67s 19.93s
% Output : CNFRefutation 33.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 7
% Syntax : Number of clauses : 76 ( 76 unt; 0 nHn; 3 RR)
% Number of literals : 76 ( 75 equ; 2 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 210 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f05,axiom,
mult(X1,mult(X2,X3)) = mult(mult(rd(X1,X1),X2),mult(X1,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(f01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(f04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(f02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(f06,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),mult(X2,ld(X3,X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
cnf(f03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(goals,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c_0_7,axiom,
mult(X1,mult(X2,X3)) = mult(mult(rd(X1,X1),X2),mult(X1,X3)),
f05 ).
cnf(c_0_8,axiom,
mult(X1,ld(X1,X2)) = X2,
f01 ).
cnf(c_0_9,axiom,
rd(mult(X1,X2),X2) = X1,
f04 ).
cnf(c_0_10,plain,
mult(mult(rd(X1,X1),X2),X3) = mult(X1,mult(X2,ld(X1,X3))),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
ld(X1,mult(X1,X2)) = X2,
f02 ).
cnf(c_0_12,axiom,
mult(mult(X1,X2),X3) = mult(mult(X1,X3),mult(X2,ld(X3,X3))),
f06 ).
cnf(c_0_13,axiom,
mult(rd(X1,X2),X2) = X1,
f03 ).
cnf(c_0_14,plain,
rd(mult(X1,mult(X2,ld(X1,X3))),X3) = mult(rd(X1,X1),X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
ld(mult(X1,X2),mult(mult(X1,X3),X2)) = mult(X3,ld(X2,X2)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_17,plain,
rd(mult(X1,mult(X2,X3)),mult(X1,X3)) = mult(rd(X1,X1),X2),
inference(spm,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_18,plain,
ld(mult(rd(X1,X1),X2),mult(X1,mult(X3,ld(X1,X2)))) = mult(X3,ld(X2,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_10]) ).
cnf(c_0_19,plain,
ld(mult(rd(X1,X1),X2),mult(X1,mult(X2,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,plain,
ld(mult(rd(X1,X1),X2),mult(X1,X3)) = mult(rd(X3,ld(X1,X2)),ld(X2,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_21,plain,
mult(rd(mult(X1,X2),ld(X3,X1)),ld(X1,X1)) = mult(X3,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_22,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X1)))) = mult(X3,mult(X2,ld(X1,ld(X3,X1)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_10]) ).
cnf(c_0_23,plain,
rd(mult(mult(X1,X2),X3),mult(X2,ld(X3,X3))) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_24,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X1)))) = mult(rd(X1,X3),mult(X2,ld(X1,X3))),
inference(spm,[status(thm)],[c_0_22,c_0_16]) ).
cnf(c_0_25,plain,
rd(mult(X1,X2),mult(X3,ld(X2,X2))) = mult(rd(X1,X3),X2),
inference(spm,[status(thm)],[c_0_23,c_0_13]) ).
cnf(c_0_26,plain,
mult(mult(X1,rd(X2,ld(X3,X3))),X3) = mult(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_27,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X1)))) = mult(rd(X1,mult(X1,X3)),mult(X2,X3)),
inference(spm,[status(thm)],[c_0_24,c_0_11]) ).
cnf(c_0_28,plain,
rd(X1,mult(X2,ld(X3,X3))) = mult(rd(rd(X1,X3),X2),X3),
inference(spm,[status(thm)],[c_0_25,c_0_13]) ).
cnf(c_0_29,plain,
mult(mult(rd(X1,X2),X3),X2) = mult(X1,mult(X3,ld(X2,X2))),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_30,plain,
mult(X1,rd(X2,ld(X3,X3))) = rd(mult(mult(X1,X3),X2),X3),
inference(spm,[status(thm)],[c_0_9,c_0_26]) ).
cnf(c_0_31,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X1)))) = mult(mult(rd(rd(X1,X3),X1),X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_12]) ).
cnf(c_0_32,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_33,plain,
rd(mult(X1,mult(X2,ld(X3,X3))),X3) = mult(rd(X1,X3),X2),
inference(spm,[status(thm)],[c_0_9,c_0_29]) ).
cnf(c_0_34,plain,
mult(ld(X1,X2),ld(X3,X3)) = ld(mult(X1,X3),mult(X2,X3)),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_35,plain,
rd(mult(mult(rd(X1,rd(X2,ld(X3,X3))),X3),X2),X3) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_30]) ).
cnf(c_0_36,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X1)))) = mult(mult(rd(X3,X1),X2),ld(X3,X1)),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
mult(rd(mult(rd(X1,X2),X3),X1),X2) = mult(rd(X1,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_28]),c_0_33]) ).
cnf(c_0_38,plain,
rd(ld(mult(X1,X2),mult(X3,X2)),ld(X2,X2)) = ld(X1,X3),
inference(spm,[status(thm)],[c_0_9,c_0_34]) ).
cnf(c_0_39,plain,
mult(X1,mult(ld(rd(X1,X1),X2),ld(X1,X3))) = mult(X2,X3),
inference(spm,[status(thm)],[c_0_10,c_0_8]) ).
cnf(c_0_40,plain,
mult(mult(rd(X1,rd(X2,ld(X3,X3))),X3),X2) = mult(X1,X3),
inference(spm,[status(thm)],[c_0_13,c_0_35]) ).
cnf(c_0_41,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X1)))) = mult(mult(X3,X2),ld(mult(X3,X1),X1)),
inference(spm,[status(thm)],[c_0_36,c_0_9]) ).
cnf(c_0_42,plain,
mult(rd(mult(X1,X2),X3),ld(X1,X3)) = mult(rd(X3,X3),X2),
inference(spm,[status(thm)],[c_0_37,c_0_32]) ).
cnf(c_0_43,plain,
rd(ld(mult(X1,X2),X3),ld(X2,X2)) = ld(X1,rd(X3,X2)),
inference(spm,[status(thm)],[c_0_38,c_0_13]) ).
cnf(c_0_44,plain,
mult(X1,mult(ld(rd(X1,X1),X2),X3)) = mult(X2,mult(X1,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_11]) ).
cnf(c_0_45,plain,
mult(rd(X1,rd(X2,ld(X3,X3))),X3) = rd(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_9,c_0_40]) ).
cnf(c_0_46,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X1)))) = mult(X3,ld(mult(rd(X3,X2),X1),X1)),
inference(spm,[status(thm)],[c_0_41,c_0_13]) ).
cnf(c_0_47,plain,
mult(rd(X1,X2),ld(X3,X2)) = mult(rd(X2,X2),ld(X3,X1)),
inference(spm,[status(thm)],[c_0_42,c_0_8]) ).
cnf(c_0_48,plain,
rd(ld(X1,X2),ld(X3,X3)) = ld(rd(X1,X3),rd(X2,X3)),
inference(spm,[status(thm)],[c_0_43,c_0_13]) ).
cnf(c_0_49,plain,
mult(ld(rd(X1,X1),X2),X3) = ld(X1,mult(X2,mult(X1,X3))),
inference(spm,[status(thm)],[c_0_11,c_0_44]) ).
cnf(c_0_50,plain,
rd(X1,rd(X2,ld(X3,X3))) = rd(rd(mult(X1,X3),X2),X3),
inference(spm,[status(thm)],[c_0_9,c_0_45]) ).
cnf(c_0_51,plain,
mult(X1,ld(rd(mult(X1,X2),X3),X2)) = mult(rd(X2,X2),X3),
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_46,c_0_47]),c_0_48]),c_0_49]),c_0_8]),c_0_8]),c_0_50]),c_0_13]) ).
cnf(c_0_52,plain,
ld(rd(mult(X1,X2),X3),X2) = ld(X1,mult(rd(X2,X2),X3)),
inference(spm,[status(thm)],[c_0_11,c_0_51]) ).
cnf(c_0_53,plain,
rd(X1,ld(X2,mult(rd(X1,X1),X3))) = rd(mult(X2,X1),X3),
inference(spm,[status(thm)],[c_0_32,c_0_52]) ).
cnf(c_0_54,plain,
ld(X1,mult(X2,mult(X3,ld(X2,ld(X2,X2))))) = mult(X3,ld(X2,ld(X1,X2))),
inference(spm,[status(thm)],[c_0_11,c_0_22]) ).
cnf(c_0_55,plain,
rd(X1,mult(X2,ld(X1,ld(X3,X1)))) = mult(rd(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_24]),c_0_54]),c_0_28]),c_0_9]) ).
cnf(c_0_56,plain,
rd(mult(rd(X1,X1),X2),X3) = rd(mult(rd(X1,X3),X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_37]) ).
cnf(c_0_57,plain,
ld(mult(rd(X1,X1),X2),mult(X1,X3)) = mult(X1,ld(X2,X3)),
inference(spm,[status(thm)],[c_0_19,c_0_8]) ).
cnf(c_0_58,plain,
ld(mult(rd(X1,X2),X3),X3) = mult(X2,ld(X3,ld(X1,X3))),
inference(spm,[status(thm)],[c_0_16,c_0_55]) ).
cnf(c_0_59,plain,
mult(rd(mult(rd(X1,X1),X2),X3),X1) = mult(rd(X1,X3),X2),
inference(spm,[status(thm)],[c_0_13,c_0_56]) ).
cnf(c_0_60,plain,
ld(mult(rd(X1,X1),X2),X3) = mult(X1,ld(X2,ld(X1,X3))),
inference(spm,[status(thm)],[c_0_57,c_0_8]) ).
cnf(c_0_61,plain,
mult(X1,mult(X2,ld(X1,mult(X3,ld(X2,X2))))) = mult(X1,mult(X3,ld(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_10]) ).
cnf(c_0_62,plain,
ld(mult(rd(X1,X2),X3),X1) = mult(X2,ld(X3,ld(X1,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),c_0_11]) ).
cnf(c_0_63,plain,
mult(X1,ld(X2,mult(X3,ld(X1,X1)))) = mult(X3,ld(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_61]),c_0_11]) ).
cnf(c_0_64,plain,
mult(ld(X1,X2),ld(X3,ld(X2,X2))) = ld(mult(X1,X3),X2),
inference(spm,[status(thm)],[c_0_62,c_0_32]) ).
cnf(c_0_65,plain,
mult(X1,ld(X2,ld(mult(X3,X1),mult(X4,X1)))) = mult(ld(X3,X4),ld(X2,X1)),
inference(spm,[status(thm)],[c_0_63,c_0_34]) ).
cnf(c_0_66,plain,
mult(ld(X1,X1),ld(X2,X3)) = ld(mult(X1,X2),mult(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_11]),c_0_65]) ).
cnf(c_0_67,plain,
ld(mult(X1,X2),mult(X1,mult(X2,X3))) = mult(ld(X1,X1),X3),
inference(spm,[status(thm)],[c_0_66,c_0_11]) ).
cnf(c_0_68,plain,
rd(mult(X1,mult(X2,X3)),mult(ld(X1,X1),X3)) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_67]) ).
cnf(c_0_69,plain,
mult(X1,mult(X2,ld(X1,ld(X1,X3)))) = mult(rd(X3,X3),mult(X2,ld(X1,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_14]),c_0_10]) ).
cnf(c_0_70,plain,
rd(mult(rd(X1,X1),X2),ld(X3,X1)) = rd(mult(X3,X2),X1),
inference(spm,[status(thm)],[c_0_9,c_0_42]) ).
cnf(c_0_71,plain,
rd(mult(mult(X1,X1),mult(X2,ld(X1,X3))),X3) = mult(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_66]),c_0_8]),c_0_70]) ).
cnf(c_0_72,plain,
mult(mult(X1,X1),mult(X2,ld(X1,X3))) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_13,c_0_71]) ).
cnf(c_0_73,negated_conjecture,
mult(mult(a,a),mult(b,c)) != mult(mult(a,b),mult(a,c)),
goals ).
cnf(c_0_74,plain,
mult(mult(X1,X1),mult(X2,X3)) = mult(mult(X1,X2),mult(X1,X3)),
inference(spm,[status(thm)],[c_0_72,c_0_11]) ).
cnf(c_0_75,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_74])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP754-1 : 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
% 0.16/0.33 % Computer : n009.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 19:04:56 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 33.67/19.93 % Version : CSE_E---1.7
% 33.67/19.93 % Problem : theBenchmark.p
% 33.67/19.93 % SZS status Unsatisfiable for theBenchmark.p
% 33.67/19.93 % SZS output start CNFRefutation
% See solution above
% 33.80/20.04 % Total time : 15.406s
%------------------------------------------------------------------------------