%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP685-10 : TPTP v9.2.1. Released v8.1.0.
% 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 : n001.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 1.42s 1.78s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of clauses : 57 ( 57 unt; 0 nHn; 5 RR)
% Number of literals : 57 ( 56 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 119 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f01,axiom,
ld(X1,mult(X1,X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
cnf(f03,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
cnf(f02,axiom,
rd(mult(X1,X1),X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
cnf(f04,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
cnf(f07,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
cnf(f05,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
cnf(f06,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
cnf(goal,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
cnf(c_0_8,axiom,
ld(X1,mult(X1,X1)) = X1,
f01 ).
cnf(c_0_9,axiom,
mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
f03 ).
cnf(c_0_10,axiom,
rd(mult(X1,X1),X1) = X1,
f02 ).
cnf(c_0_11,axiom,
mult(rd(X1,X2),X2) = rd(mult(X1,X2),X2),
f04 ).
cnf(c_0_12,axiom,
ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
f07 ).
cnf(c_0_13,plain,
mult(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_14,axiom,
ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
f05 ).
cnf(c_0_15,plain,
mult(rd(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_11]),c_0_9]) ).
cnf(c_0_17,plain,
mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_13]) ).
cnf(c_0_18,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_14,c_0_9]),c_0_9]) ).
cnf(c_0_19,axiom,
rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
f06 ).
cnf(c_0_20,plain,
rd(X1,X1) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_15]),c_0_16]),c_0_17]) ).
cnf(c_0_21,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_18,c_0_9]) ).
cnf(c_0_22,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_19,c_0_11]),c_0_11]) ).
cnf(c_0_23,plain,
mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[c_0_16,c_0_20]) ).
cnf(c_0_24,plain,
mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_25,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,X3)),ld(X3,X3)),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_26,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(X1,mult(X1,ld(X1,ld(X3,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_13]),c_0_23]) ).
cnf(c_0_27,plain,
mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_13]),c_0_9]) ).
cnf(c_0_28,plain,
mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_24]),c_0_13]) ).
cnf(c_0_29,plain,
mult(rd(X1,rd(X2,X3)),rd(X2,X3)) = mult(X1,ld(X3,X3)),
inference(rw,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,plain,
mult(ld(X1,X1),X1) = X1,
inference(rw,[status(thm)],[c_0_15,c_0_20]) ).
cnf(c_0_31,plain,
mult(X1,ld(X1,mult(X2,ld(mult(X1,ld(X1,X2)),X3)))) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_9]),c_0_24]) ).
cnf(c_0_32,plain,
mult(rd(X1,X2),ld(X2,X2)) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_30]) ).
cnf(c_0_33,plain,
ld(mult(X1,ld(X1,X2)),mult(X1,ld(X1,mult(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_24]),c_0_24]),c_0_31]) ).
cnf(c_0_34,plain,
mult(ld(X1,X2),mult(X1,ld(X1,X3))) = mult(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_35,plain,
mult(rd(X1,rd(X2,X1)),rd(X2,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_13]) ).
cnf(c_0_36,plain,
mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_37,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_38,plain,
mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_33]) ).
cnf(c_0_39,plain,
mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_13,c_0_28]) ).
cnf(c_0_40,plain,
rd(X1,ld(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_20]),c_0_36]) ).
cnf(c_0_41,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_37]),c_0_13]) ).
cnf(c_0_42,plain,
ld(X1,mult(X2,ld(X2,X3))) = ld(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_38]),c_0_9]),c_0_39]),c_0_39]) ).
cnf(c_0_43,plain,
mult(X1,mult(rd(X2,mult(X1,X2)),mult(X1,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_22,c_0_35]) ).
cnf(c_0_44,plain,
mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_40]),c_0_41]) ).
cnf(c_0_45,plain,
ld(mult(X1,ld(X1,X2)),mult(X2,X3)) = mult(X1,ld(X1,X3)),
inference(rw,[status(thm)],[c_0_33,c_0_42]) ).
cnf(c_0_46,plain,
mult(X1,mult(X2,ld(mult(X1,X2),mult(X1,X2)))) = mult(X1,X2),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
ld(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,ld(X2,X3))),
inference(spm,[status(thm)],[c_0_42,c_0_45]) ).
cnf(c_0_48,plain,
mult(X1,mult(X2,ld(X2,X3))) = mult(X1,X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_42]),c_0_27]) ).
cnf(c_0_49,negated_conjecture,
rd(mult(x6,ld(x7,x8)),ld(x7,x8)) != rd(mult(x6,x8),x8),
goal ).
cnf(c_0_50,plain,
mult(X1,mult(ld(X1,X2),ld(X2,X2))) = mult(X1,ld(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_42]),c_0_48]) ).
cnf(c_0_51,plain,
mult(X1,ld(X1,mult(ld(X1,X2),X3))) = mult(ld(X1,X2),X3),
inference(spm,[status(thm)],[c_0_24,c_0_39]) ).
cnf(c_0_52,negated_conjecture,
mult(rd(x6,ld(x7,x8)),ld(x7,x8)) != mult(rd(x6,x8),x8),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_11]),c_0_11]) ).
cnf(c_0_53,plain,
mult(ld(X1,X2),ld(X2,X2)) = ld(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_50]),c_0_9]),c_0_39]),c_0_51]) ).
cnf(c_0_54,negated_conjecture,
mult(x6,ld(ld(x7,x8),ld(x7,x8))) != mult(x6,ld(x8,x8)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_52,c_0_44]),c_0_44]) ).
cnf(c_0_55,plain,
ld(ld(X1,X2),ld(X1,X2)) = mult(X1,ld(X1,ld(X2,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_53]),c_0_28]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_54,c_0_55]),c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP685-10 : TPTP v9.2.1. Released v8.1.0.
% 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
% 0.17/0.34 % Computer : n001.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 19:02:48 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 1.42/1.78 % Version : CSE_E---1.7
% 1.42/1.78 % Problem : theBenchmark.p
% 1.42/1.78 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.78 % SZS output start CNFRefutation
% See solution above
% 1.42/1.78 % Total time : 1.368s
%------------------------------------------------------------------------------