%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP710+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 : n017.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 04:27:08 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 32 unt; 0 def)
% Number of atoms : 52 ( 42 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 26 ( 16 ~; 6 |; 2 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 67 ( 6 sgn 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f01,axiom,
! [X1] : mult(X1,unit) = X1,
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f05,axiom,
! [X1] : mult(i(X1),X1) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f02,axiom,
! [X1] : mult(unit,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f04,axiom,
! [X1] : mult(X1,i(X1)) = unit,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(goals,conjecture,
( ! [X4,X5] :
? [X6] : mult(X4,X6) = X5
& ! [X7,X8] :
? [X9] : mult(X9,X8) = X7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_6,plain,
! [X23] : mult(X23,unit) = X23,
inference(variable_rename,[status(thm)],[f01]) ).
fof(c_0_7,plain,
! [X25,X26,X27] : mult(X27,mult(X26,mult(X26,X25))) = mult(mult(mult(X27,X26),X26),X25),
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_8,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
mult(X1,mult(X2,mult(X2,X3))) = mult(mult(mult(X1,X2),X2),X3),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_8]) ).
fof(c_0_11,plain,
! [X29] : mult(i(X29),X29) = unit,
inference(variable_rename,[status(thm)],[f05]) ).
fof(c_0_12,plain,
! [X24] : mult(unit,X24) = X24,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_13,plain,
! [X28] : mult(X28,i(X28)) = unit,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_14,plain,
mult(mult(X1,mult(X2,X2)),X3) = mult(X1,mult(X2,mult(X2,X3))),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
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,plain,
mult(X1,i(X1)) = unit,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
mult(i(mult(X1,X1)),mult(X1,mult(X1,X2))) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,plain,
mult(X1,mult(i(X1),i(X1))) = i(X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_17]),c_0_16]) ).
cnf(c_0_20,plain,
mult(i(X1),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_15]),c_0_16]) ).
cnf(c_0_21,plain,
i(mult(X1,X1)) = mult(i(X1),i(X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_17]),c_0_8]) ).
cnf(c_0_22,plain,
mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_16]),c_0_16]) ).
cnf(c_0_23,plain,
mult(i(X1),mult(X1,mult(X1,X2))) = mult(X1,X2),
inference(spm,[status(thm)],[c_0_14,c_0_20]) ).
fof(c_0_24,negated_conjecture,
~ ( ! [X4,X5] :
? [X6] : mult(X4,X6) = X5
& ! [X7,X8] :
? [X9] : mult(X9,X8) = X7 ),
inference(assume_negation,[status(cth)],[goals]) ).
fof(c_0_25,plain,
( ~ epred2_0
<=> ! [X1] : mult(esk1_0,X1) != esk2_0 ),
introduced(definition) ).
cnf(c_0_26,plain,
mult(i(X1),mult(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_27,plain,
i(i(X1)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_20]),c_0_15]),c_0_8]) ).
fof(c_0_28,negated_conjecture,
! [X32,X35] :
( mult(esk1_0,X32) != esk2_0
| mult(X35,esk4_0) != esk3_0 ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_29,negated_conjecture,
( epred2_0
| mult(esk1_0,X1) != esk2_0 ),
inference(split_equiv,[status(thm)],[c_0_25]) ).
cnf(c_0_30,plain,
mult(X1,mult(i(X1),X2)) = X2,
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_31,plain,
( ~ epred1_0
<=> ! [X2] : mult(X2,esk4_0) != esk3_0 ),
introduced(definition) ).
cnf(c_0_32,negated_conjecture,
( mult(esk1_0,X1) != esk2_0
| mult(X2,esk4_0) != esk3_0 ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,negated_conjecture,
( epred2_0
| X1 != esk2_0 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_34,plain,
mult(mult(X1,mult(X2,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X2,mult(X3,X3)))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_14]) ).
cnf(c_0_35,negated_conjecture,
( ~ epred2_0
| ~ epred1_0 ),
inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_32,c_0_31]),c_0_25]) ).
cnf(c_0_36,negated_conjecture,
epred2_0,
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,negated_conjecture,
( epred1_0
| mult(X1,esk4_0) != esk3_0 ),
inference(split_equiv,[status(thm)],[c_0_31]) ).
cnf(c_0_38,plain,
mult(mult(X1,i(X2)),X2) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_15]),c_0_8]),c_0_26]),c_0_15]),c_0_8]) ).
cnf(c_0_39,negated_conjecture,
~ epred1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_36])]) ).
cnf(c_0_40,negated_conjecture,
X1 != esk3_0,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_41,negated_conjecture,
$false,
inference(er,[status(thm)],[c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : GRP710+1 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % 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
% 0.15/0.34 % Computer : n017.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon May 4 19:01:58 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.369s
%------------------------------------------------------------------------------