%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP711+1 : TPTP v9.2.1. Released v4.0.0.
% 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 : n026.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 04:27:09 PM UTC 2026
% Result : Theorem 1.34s 1.74s
% Output : CNFRefutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 26 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 25 ( 8 ~; 8 |; 5 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X1] : mult(X1,unit) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f01) ).
fof(f03,axiom,
! [X2,X3,X1] : mult(X1,mult(X3,mult(X3,X2))) = mult(mult(mult(X1,X3),X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f03) ).
fof(goals,conjecture,
! [X4,X5,X6] :
( ( mult(X4,X5) = mult(X4,X6)
=> X5 = X6 )
& ( mult(X5,X4) = mult(X6,X4)
=> X5 = X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(f05,axiom,
! [X1] : mult(i(X1),X1) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).
fof(f02,axiom,
! [X1] : mult(unit,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f02) ).
fof(f04,axiom,
! [X1] : mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f04) ).
fof(c_0_6,plain,
! [X17] : mult(X17,unit) = X17,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_7,plain,
! [X19,X20,X21] : mult(X21,mult(X20,mult(X20,X19))) = mult(mult(mult(X21,X20),X20),X19),
inference(variable_rename,[status(thm)],[f03]) ).
fof(c_0_8,negated_conjecture,
~ ! [X4,X5,X6] :
( ( mult(X4,X5) = mult(X4,X6)
=> X5 = X6 )
& ( mult(X5,X4) = mult(X6,X4)
=> X5 = X6 ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_9,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X23] : mult(i(X23),X23) = unit,
inference(variable_rename,[status(thm)],[f05]) ).
fof(c_0_12,plain,
! [X18] : mult(unit,X18) = X18,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_13,negated_conjecture,
( ( mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0)
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) )
& ( esk2_0 != esk3_0
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) )
& ( mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0)
| esk2_0 != esk3_0 )
& ( esk2_0 != esk3_0
| esk2_0 != esk3_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
cnf(c_0_14,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_9]) ).
cnf(c_0_15,plain,
mult(i(X1),X1) = unit,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( mult(esk2_0,esk1_0) = mult(esk3_0,esk1_0)
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X22] : mult(X22,i(X22)) = unit,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_19,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[c_0_10,c_0_14]) ).
cnf(c_0_20,plain,
mult(i(X1),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( mult(esk2_0,mult(esk1_0,esk1_0)) = mult(esk3_0,mult(esk1_0,esk1_0))
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_17]),c_0_14]) ).
cnf(c_0_22,plain,
mult(X1,i(X1)) = unit,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,negated_conjecture,
( esk2_0 != esk3_0
| esk2_0 != esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_24,plain,
mult(mult(X1,mult(X2,mult(X2,mult(X3,X3)))),X4) = mult(X1,mult(X2,mult(X2,mult(X3,mult(X3,X4))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_19]),c_0_19]) ).
cnf(c_0_25,plain,
mult(i(X1),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
( mult(esk2_0,mult(esk1_0,mult(esk1_0,X1))) = mult(esk3_0,mult(esk1_0,mult(esk1_0,X1)))
| mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_21]),c_0_19]) ).
cnf(c_0_27,plain,
mult(X1,mult(i(X1),i(X1))) = i(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_22]),c_0_16]) ).
cnf(c_0_28,negated_conjecture,
esk3_0 != esk2_0,
inference(cn,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
mult(X1,mult(i(X2),mult(X2,X3))) = mult(X1,X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_15]),c_0_9]),c_0_25]) ).
cnf(c_0_30,negated_conjecture,
mult(esk1_0,esk2_0) = mult(esk1_0,esk3_0),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_22]),c_0_9]),c_0_22]),c_0_9]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
mult(X1,esk2_0) = mult(X1,esk3_0),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_31]),c_0_16]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP711+1 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.14/0.33 % Computer : n026.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 19:03:38 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.34/1.74 % Version : CSE_E---1.7
% 1.34/1.74 % Problem : theBenchmark.p
% 1.34/1.74 % SZS status Theorem for theBenchmark.p
% 1.34/1.74 % SZS output start CNFRefutation
% See solution above
% 1.34/1.74 % Total time : 1.371s
%------------------------------------------------------------------------------