%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP660-12 : TPTP v9.2.1. Released v8.1.0.
% 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 : n003.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 04:26:47 PM UTC 2026
% Result : Unsatisfiable 7.37s 5.56s
% Output : CNFRefutation 7.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 6
% Syntax : Number of clauses : 65 ( 65 unt; 0 nHn; 3 RR)
% Number of literals : 65 ( 64 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(f04,axiom,
rd(mult(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
cnf(f05,axiom,
mult(mult(mult(X1,X2),X3),X1) = mult(X1,mult(X2,mult(X3,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
cnf(f03,axiom,
mult(rd(X1,X2),X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
cnf(f01,axiom,
mult(X1,ld(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
cnf(f02,axiom,
ld(X1,mult(X1,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
cnf(goal,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goal) ).
cnf(c_0_6,axiom,
rd(mult(X1,X2),X2) = X1,
f04 ).
cnf(c_0_7,axiom,
mult(mult(mult(X1,X2),X3),X1) = mult(X1,mult(X2,mult(X3,X1))),
f05 ).
cnf(c_0_8,plain,
rd(mult(X1,mult(X2,mult(X3,X1))),X1) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,axiom,
mult(rd(X1,X2),X2) = X1,
f03 ).
cnf(c_0_10,plain,
rd(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),rd(X3,X1)),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,plain,
mult(mult(mult(X1,X2),X1),rd(X2,mult(X1,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_12,plain,
mult(mult(X1,rd(X2,X3)),rd(X3,X1)) = rd(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_13,plain,
mult(mult(X1,rd(X1,X2)),rd(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_14,plain,
mult(rd(X1,X2),mult(X2,mult(X3,rd(X1,X2)))) = mult(mult(X1,X3),rd(X1,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_9]) ).
cnf(c_0_15,plain,
rd(rd(mult(X1,X2),X1),rd(X3,X1)) = mult(X1,rd(X2,X3)),
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
cnf(c_0_16,plain,
rd(X1,rd(X2,X1)) = mult(X1,rd(X1,X2)),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_17,axiom,
mult(X1,ld(X1,X2)) = X2,
f01 ).
cnf(c_0_18,axiom,
ld(X1,mult(X1,X2)) = X2,
f02 ).
cnf(c_0_19,plain,
rd(mult(mult(X1,X2),rd(X1,X3)),mult(X3,mult(X2,rd(X1,X3)))) = rd(X1,X3),
inference(spm,[status(thm)],[c_0_6,c_0_14]) ).
cnf(c_0_20,plain,
rd(rd(mult(X1,X2),X1),X3) = mult(X1,rd(X2,mult(X3,X1))),
inference(spm,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_21,plain,
mult(X1,rd(X1,mult(X2,X1))) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_16,c_0_6]) ).
cnf(c_0_22,plain,
mult(mult(X1,X2),rd(ld(X2,X3),X1)) = rd(mult(X1,X3),X1),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_23,plain,
mult(X1,mult(ld(X1,X2),mult(X3,X1))) = mult(mult(X2,X3),X1),
inference(spm,[status(thm)],[c_0_7,c_0_17]) ).
cnf(c_0_24,plain,
mult(mult(X1,X2),rd(ld(X2,X1),X1)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_25,plain,
ld(mult(X1,rd(X1,X2)),X1) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_18,c_0_13]) ).
cnf(c_0_26,plain,
mult(X1,rd(X2,mult(mult(X1,mult(rd(X2,X1),rd(X1,X1))),X1))) = rd(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_12]),c_0_20]) ).
cnf(c_0_27,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_28,plain,
ld(X1,rd(X1,X2)) = rd(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_29,plain,
ld(mult(X1,X2),rd(mult(X1,X3),X1)) = rd(ld(X2,X3),X1),
inference(spm,[status(thm)],[c_0_18,c_0_22]) ).
cnf(c_0_30,plain,
ld(X1,mult(mult(X2,X3),X1)) = mult(ld(X1,X2),mult(X3,X1)),
inference(spm,[status(thm)],[c_0_18,c_0_23]) ).
cnf(c_0_31,plain,
rd(ld(X1,X2),X2) = ld(mult(X2,X1),X2),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_32,plain,
mult(X1,mult(ld(X1,X2),X3)) = mult(mult(X2,rd(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_23,c_0_9]) ).
cnf(c_0_33,plain,
mult(X1,mult(rd(X1,X1),rd(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_6]) ).
cnf(c_0_34,plain,
rd(mult(X1,X2),mult(X1,mult(X1,X2))) = rd(ld(X2,X2),X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
mult(ld(X1,X2),mult(ld(X2,X3),X1)) = ld(X1,mult(X3,X1)),
inference(spm,[status(thm)],[c_0_30,c_0_17]) ).
cnf(c_0_36,plain,
ld(ld(mult(X1,X2),X1),ld(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_31]) ).
cnf(c_0_37,plain,
mult(mult(rd(X1,X2),rd(X3,X1)),X1) = mult(X1,mult(rd(X1,mult(X2,X1)),X3)),
inference(spm,[status(thm)],[c_0_32,c_0_28]) ).
cnf(c_0_38,plain,
mult(rd(X1,X1),rd(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_18,c_0_33]) ).
cnf(c_0_39,plain,
rd(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_18]),c_0_6]) ).
cnf(c_0_40,plain,
ld(rd(X1,mult(X2,X1)),ld(X2,rd(X1,X2))) = rd(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_9]),c_0_28]) ).
cnf(c_0_41,plain,
mult(X1,mult(rd(X1,mult(X1,X1)),X1)) = mult(ld(X1,X1),X1),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_39]) ).
cnf(c_0_43,plain,
ld(rd(X1,mult(X1,X1)),rd(X1,mult(X1,X1))) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_28]) ).
cnf(c_0_44,plain,
mult(X1,rd(ld(X1,X2),mult(X3,X1))) = rd(rd(X2,X1),X3),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_45,plain,
ld(X1,mult(ld(X1,X1),X1)) = mult(rd(X1,mult(X1,X1)),X1),
inference(spm,[status(thm)],[c_0_18,c_0_41]) ).
cnf(c_0_46,plain,
ld(X1,X1) = rd(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_38]) ).
cnf(c_0_47,plain,
rd(rd(X1,X2),rd(X3,X2)) = mult(X2,rd(ld(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_44,c_0_9]) ).
cnf(c_0_48,plain,
mult(rd(X1,mult(X1,X1)),X1) = rd(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_9]),c_0_46]) ).
cnf(c_0_49,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_6,c_0_17]) ).
cnf(c_0_50,plain,
mult(X1,rd(ld(X1,mult(X2,X1)),X3)) = rd(X2,rd(X3,X1)),
inference(spm,[status(thm)],[c_0_47,c_0_6]) ).
cnf(c_0_51,plain,
mult(X1,rd(ld(X2,X3),rd(X1,X2))) = rd(mult(rd(X1,X2),X3),rd(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_52,plain,
mult(X1,rd(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_46]) ).
cnf(c_0_53,plain,
rd(rd(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(spm,[status(thm)],[c_0_6,c_0_48]) ).
cnf(c_0_54,plain,
rd(X1,mult(ld(X2,X1),X1)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_28,c_0_49]) ).
cnf(c_0_55,plain,
rd(X1,rd(X2,mult(X2,X2))) = mult(mult(rd(X2,X2),X1),X2),
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_10]),c_0_16]),c_0_52]),c_0_53]) ).
cnf(c_0_56,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(rw,[status(thm)],[c_0_38,c_0_46]) ).
cnf(c_0_57,plain,
ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
inference(spm,[status(thm)],[c_0_27,c_0_54]) ).
cnf(c_0_58,plain,
ld(mult(mult(X1,X2),X3),mult(X1,mult(X2,mult(X3,X1)))) = X1,
inference(spm,[status(thm)],[c_0_18,c_0_7]) ).
cnf(c_0_59,plain,
mult(mult(rd(X1,X1),X2),rd(X1,X1)) = rd(X2,rd(X1,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_47]),c_0_46]),c_0_53]),c_0_21]),c_0_47]),c_0_46]),c_0_53]),c_0_21]) ).
cnf(c_0_60,plain,
mult(ld(mult(X1,mult(X2,mult(X3,X1))),mult(mult(X1,X2),X3)),mult(mult(X1,X2),X3)) = ld(X1,mult(mult(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_61,plain,
mult(rd(X1,X1),mult(X2,rd(X1,X1))) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_59]),c_0_9]),c_0_38]),c_0_46]) ).
cnf(c_0_62,negated_conjecture,
mult(rd(x1,x1),x0) != x0,
goal ).
cnf(c_0_63,plain,
mult(rd(X1,X1),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_60,c_0_61]),c_0_38]),c_0_46]),c_0_46]),c_0_38]),c_0_46]),c_0_9]),c_0_38]),c_0_46]),c_0_18]) ).
cnf(c_0_64,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP660-12 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.11 % 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
% 0.16/0.32 % Computer : n003.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 18:59:41 EDT 2026
% 0.16/0.32 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 7.37/5.56 % Version : CSE_E---1.7
% 7.37/5.56 % Problem : theBenchmark.p
% 7.37/5.56 % SZS status Unsatisfiable for theBenchmark.p
% 7.37/5.56 % SZS output start CNFRefutation
% See solution above
% 7.37/5.58 % Total time : 4.371s
%------------------------------------------------------------------------------