%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP660+2 : 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 : n015.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 04:26:48 PM UTC 2026
% Result : Theorem 3.89s 3.17s
% Output : CNFRefutation 3.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 6
% Syntax : Number of formulae : 66 ( 61 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 12 ( 7 ~; 3 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 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 : 131 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f05,axiom,
! [X3,X1,X2] : mult(mult(mult(X2,X1),X3),X2) = mult(X2,mult(X1,mult(X3,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(goals,conjecture,
! [X4,X5] :
( mult(X4,rd(X5,X5)) = X4
& mult(rd(X5,X5),X4) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_6,plain,
! [X25,X26] : rd(mult(X26,X25),X25) = X26,
inference(variable_rename,[status(thm)],[f04]) ).
fof(c_0_7,plain,
! [X27,X28,X29] : mult(mult(mult(X29,X28),X27),X29) = mult(X29,mult(X28,mult(X27,X29))),
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_8,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
mult(mult(mult(X1,X2),X3),X1) = mult(X1,mult(X2,mult(X3,X1))),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_10,plain,
! [X23,X24] : mult(rd(X24,X23),X23) = X24,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_11,plain,
rd(mult(X1,mult(X2,mult(X3,X1))),X1) = mult(mult(X1,X2),X3),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_12,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
rd(mult(X1,mult(X2,X3)),X1) = mult(mult(X1,X2),rd(X3,X1)),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,plain,
mult(mult(X1,rd(X2,X3)),rd(X3,X1)) = rd(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
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_8,c_0_14]) ).
fof(c_0_16,plain,
! [X19,X20] : mult(X20,ld(X20,X19)) = X19,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_17,plain,
! [X21,X22] : ld(X22,mult(X22,X21)) = X21,
inference(variable_rename,[status(thm)],[f02]) ).
cnf(c_0_18,plain,
rd(X1,rd(X2,X1)) = mult(X1,rd(X1,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_8]) ).
cnf(c_0_19,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
mult(X1,rd(X1,mult(X2,X1))) = rd(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
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_13,c_0_19]) ).
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_9,c_0_19]) ).
cnf(c_0_24,plain,
ld(X1,rd(X1,X2)) = rd(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
ld(mult(X1,X2),rd(mult(X1,X3),X1)) = rd(ld(X2,X3),X1),
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
cnf(c_0_26,plain,
ld(X1,mult(mult(X2,X3),X1)) = mult(ld(X1,X2),mult(X3,X1)),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_27,plain,
rd(mult(X1,X2),mult(X1,mult(X1,X2))) = rd(ld(X2,X2),X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,plain,
mult(ld(X1,X2),mult(ld(X2,X3),X1)) = ld(X1,mult(X3,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_19]) ).
cnf(c_0_29,plain,
ld(rd(X1,X2),X1) = X2,
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_30,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_27,c_0_28]),c_0_20]),c_0_8]) ).
cnf(c_0_31,plain,
ld(mult(X1,rd(X1,X2)),X1) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_32,plain,
rd(X1,ld(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_19]) ).
cnf(c_0_33,plain,
rd(ld(X1,ld(X2,X3)),X2) = ld(mult(X2,X1),rd(X3,X2)),
inference(spm,[status(thm)],[c_0_25,c_0_19]) ).
cnf(c_0_34,plain,
ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_35,plain,
rd(ld(X1,X2),X2) = ld(mult(X2,X1),X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
ld(mult(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_19]),c_0_24]) ).
cnf(c_0_37,plain,
mult(mult(X1,X1),rd(X1,mult(X1,X1))) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_36]) ).
cnf(c_0_38,plain,
mult(mult(X1,X1),rd(X1,X1)) = mult(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_29]),c_0_29]),c_0_21]) ).
cnf(c_0_39,plain,
rd(X1,mult(ld(X2,X1),X1)) = ld(X1,X2),
inference(spm,[status(thm)],[c_0_24,c_0_32]) ).
cnf(c_0_40,plain,
mult(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_30]),c_0_30]),c_0_30]) ).
cnf(c_0_41,plain,
ld(mult(X1,X1),mult(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_38]) ).
cnf(c_0_42,plain,
ld(ld(X1,X2),X1) = mult(ld(X2,X1),X1),
inference(spm,[status(thm)],[c_0_29,c_0_39]) ).
cnf(c_0_43,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_9,c_0_12]) ).
cnf(c_0_44,plain,
mult(rd(X1,X1),rd(X1,X1)) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,plain,
mult(rd(X1,mult(X2,X1)),rd(X1,X2)) = ld(X2,rd(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_29]),c_0_24]) ).
cnf(c_0_46,plain,
mult(rd(X1,X1),mult(X1,rd(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_14]),c_0_8]) ).
cnf(c_0_47,plain,
mult(X1,rd(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_8]),c_0_12]),c_0_8]),c_0_29]) ).
cnf(c_0_48,plain,
ld(X1,X1) = rd(X1,X1),
inference(spm,[status(thm)],[c_0_20,c_0_47]) ).
cnf(c_0_49,plain,
mult(ld(X1,rd(X2,X3)),mult(X3,X1)) = ld(X1,mult(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_50,plain,
ld(rd(X1,X2),mult(X3,rd(X1,X2))) = mult(X2,mult(ld(X1,X3),rd(X1,X2))),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_51,plain,
mult(X1,mult(ld(X1,X2),X3)) = mult(mult(X2,rd(X3,X1)),X1),
inference(spm,[status(thm)],[c_0_23,c_0_12]) ).
cnf(c_0_52,plain,
rd(rd(X1,X1),X1) = rd(X1,mult(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_48]),c_0_36]) ).
cnf(c_0_53,plain,
mult(ld(rd(X1,X1),rd(X2,X1)),X1) = mult(mult(X2,rd(X1,mult(X1,X1))),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_47]),c_0_50]),c_0_51]),c_0_52]) ).
fof(c_0_54,negated_conjecture,
~ ! [X4,X5] :
( mult(X4,rd(X5,X5)) = X4
& mult(rd(X5,X5),X4) = X4 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_55,plain,
ld(mult(mult(X1,X2),X3),mult(X1,mult(X2,mult(X3,X1)))) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_9]) ).
cnf(c_0_56,plain,
ld(rd(X1,X1),rd(X2,X1)) = mult(X2,rd(X1,mult(X1,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_53]),c_0_8]) ).
fof(c_0_57,negated_conjecture,
( mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0
| mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])]) ).
cnf(c_0_58,plain,
ld(mult(mult(X1,X2),ld(X2,X3)),mult(X1,mult(mult(X3,rd(X1,X2)),X2))) = X1,
inference(spm,[status(thm)],[c_0_55,c_0_51]) ).
cnf(c_0_59,plain,
mult(rd(X1,X1),mult(X2,rd(X1,mult(X1,X1)))) = rd(X2,X1),
inference(spm,[status(thm)],[c_0_19,c_0_56]) ).
cnf(c_0_60,plain,
mult(rd(X1,X1),rd(X1,mult(X1,X1))) = rd(X1,mult(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_47]),c_0_52]),c_0_52]) ).
cnf(c_0_61,plain,
rd(rd(X1,X2),rd(X1,mult(X2,X1))) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_21]) ).
cnf(c_0_62,negated_conjecture,
( mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0
| mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_57]) ).
cnf(c_0_63,plain,
rd(X1,X1) = rd(X2,X2),
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_60]),c_0_19]),c_0_61]),c_0_8]),c_0_48]) ).
cnf(c_0_64,negated_conjecture,
( mult(esk1_0,rd(X1,X1)) != esk1_0
| mult(rd(X1,X1),esk1_0) != esk1_0 ),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_12]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP660+2 : 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 : n015.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 19:00:17 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 3.89/3.17 % Version : CSE_E---1.7
% 3.89/3.17 % Problem : theBenchmark.p
% 3.89/3.17 % SZS status Theorem for theBenchmark.p
% 3.89/3.17 % SZS output start CNFRefutation
% See solution above
% 3.89/3.18 % Total time : 2.375s
%------------------------------------------------------------------------------