%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP657+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 : n016.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 04:26:46 PM UTC 2026
% Result : Theorem 1.24s 1.71s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 20 unt; 0 def)
% Number of atoms : 28 ( 27 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 0 con; 1-2 aty)
% Number of variables : 49 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(f05,axiom,
! [X3,X1,X2] : mult(mult(X2,X1),mult(X3,X2)) = mult(X2,mult(mult(X1,X3),X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f01,axiom,
! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(goals,conjecture,
? [X4] :
! [X5] :
( mult(X5,X4) = X5
& mult(X4,X5) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c_0_5,plain,
! [X21,X22] : ld(X22,mult(X22,X21)) = X21,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_6,plain,
! [X27,X28,X29] : mult(mult(X29,X28),mult(X27,X29)) = mult(X29,mult(mult(X28,X27),X29)),
inference(variable_rename,[status(thm)],[f05]) ).
cnf(c_0_7,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
mult(mult(X1,X2),mult(X3,X1)) = mult(X1,mult(mult(X2,X3),X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_9,plain,
! [X19,X20] : mult(X20,ld(X20,X19)) = X19,
inference(variable_rename,[status(thm)],[f01]) ).
cnf(c_0_10,plain,
ld(X1,mult(mult(X1,X2),mult(X3,X1))) = mult(mult(X2,X3),X1),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,plain,
mult(X1,ld(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_12,plain,
! [X25,X26] : rd(mult(X26,X25),X25) = X26,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_13,plain,
ld(X1,mult(X2,mult(X3,X1))) = mult(mult(ld(X1,X2),X3),X1),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
mult(mult(ld(X1,X1),X2),X1) = mult(X2,X1),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
fof(c_0_16,negated_conjecture,
~ ? [X4] :
! [X5] :
( mult(X5,X4) = X5
& mult(X4,X5) = X5 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_17,plain,
mult(ld(X1,X1),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_14]) ).
fof(c_0_18,negated_conjecture,
! [X30] :
( mult(esk1_1(X30),X30) != esk1_1(X30)
| mult(X30,esk2_1(X30)) != esk2_1(X30) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
cnf(c_0_19,plain,
rd(X1,X1) = ld(X2,X2),
inference(spm,[status(thm)],[c_0_14,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( mult(esk1_1(X1),X1) != esk1_1(X1)
| mult(X1,esk2_1(X1)) != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_21,plain,
mult(rd(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_22,plain,
mult(X1,rd(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_11,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP657+1 : 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
% 0.16/0.32 % Computer : n016.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
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 18:59:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.24/1.71 % Version : CSE_E---1.7
% 1.24/1.71 % Problem : theBenchmark.p
% 1.24/1.71 % SZS status Theorem for theBenchmark.p
% 1.24/1.71 % SZS output start CNFRefutation
% See solution above
% 1.24/1.71 % Total time : 1.371s
%------------------------------------------------------------------------------