%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP700+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 : n002.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 04:27:06 PM UTC 2026
% Result : Theorem 1.57s 1.80s
% Output : CNFRefutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 37 unt; 0 def)
% Number of atoms : 45 ( 44 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 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 : 68 ( 0 sgn 31 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f08,axiom,
! [X3,X1,X2] : mult(mult(X2,X1),mult(X1,mult(X3,X1))) = mult(mult(X2,mult(X1,mult(X1,X3))),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).
fof(f05,axiom,
! [X2] : mult(X2,unit) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).
fof(f06,axiom,
! [X2] : mult(unit,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).
fof(f04,axiom,
! [X1,X2] : rd(mult(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).
fof(f03,axiom,
! [X1,X2] : mult(rd(X2,X1),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).
fof(f07,axiom,
! [X3,X1,X2] : mult(mult(mult(X2,X1),X2),mult(X2,X3)) = mult(X2,mult(mult(mult(X1,X2),X2),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).
fof(goals,conjecture,
! [X4] :
? [X5] :
( mult(X5,X4) = unit
& mult(X4,X5) = unit ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(f02,axiom,
! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).
fof(c_0_8,plain,
! [X37,X38,X39] : mult(mult(X39,X38),mult(X38,mult(X37,X38))) = mult(mult(X39,mult(X38,mult(X38,X37))),X38),
inference(variable_rename,[status(thm)],[f08]) ).
fof(c_0_9,plain,
! [X32] : mult(X32,unit) = X32,
inference(variable_rename,[status(thm)],[f05]) ).
fof(c_0_10,plain,
! [X33] : mult(unit,X33) = X33,
inference(variable_rename,[status(thm)],[f06]) ).
fof(c_0_11,plain,
! [X30,X31] : rd(mult(X31,X30),X30) = X31,
inference(variable_rename,[status(thm)],[f04]) ).
cnf(c_0_12,plain,
mult(mult(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,mult(X2,mult(X2,X3))),X2),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
rd(mult(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
mult(mult(X1,mult(X2,X2)),X2) = mult(mult(X1,X2),mult(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]) ).
fof(c_0_17,plain,
! [X28,X29] : mult(rd(X29,X28),X28) = X29,
inference(variable_rename,[status(thm)],[f03]) ).
cnf(c_0_18,plain,
rd(mult(mult(X1,X2),mult(X2,X2)),X2) = mult(X1,mult(X2,X2)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
mult(rd(X1,X2),X2) = X1,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_20,plain,
rd(mult(X1,mult(X2,X2)),X2) = mult(rd(X1,X2),mult(X2,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,plain,
mult(rd(unit,X1),mult(X1,X1)) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_14]),c_0_15]) ).
cnf(c_0_22,plain,
rd(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
fof(c_0_23,plain,
! [X34,X35,X36] : mult(mult(mult(X36,X35),X36),mult(X36,X34)) = mult(X36,mult(mult(mult(X35,X36),X36),X34)),
inference(variable_rename,[status(thm)],[f07]) ).
cnf(c_0_24,plain,
mult(rd(rd(unit,X1),X1),mult(X1,X1)) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,plain,
mult(mult(mult(X1,X2),X1),mult(X1,X3)) = mult(X1,mult(mult(mult(X2,X1),X1),X3)),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_26,plain,
rd(rd(unit,X1),X1) = rd(unit,mult(X1,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_24]) ).
fof(c_0_27,negated_conjecture,
~ ! [X4] :
? [X5] :
( mult(X5,X4) = unit
& mult(X4,X5) = unit ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_28,plain,
rd(mult(X1,mult(mult(mult(X2,X1),X1),X3)),mult(X1,X3)) = mult(mult(X1,X2),X1),
inference(spm,[status(thm)],[c_0_15,c_0_25]) ).
cnf(c_0_29,plain,
mult(rd(unit,mult(X1,X1)),X1) = rd(unit,X1),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
fof(c_0_30,plain,
! [X26,X27] : ld(X27,mult(X27,X26)) = X26,
inference(variable_rename,[status(thm)],[f02]) ).
fof(c_0_31,negated_conjecture,
! [X41] :
( mult(X41,esk1_0) != unit
| mult(esk1_0,X41) != unit ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).
cnf(c_0_32,plain,
mult(mult(X1,rd(unit,mult(X1,X1))),X1) = unit,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19]),c_0_14]),c_0_22]) ).
cnf(c_0_33,plain,
mult(mult(X1,mult(X1,X2)),X1) = mult(X1,mult(X1,mult(X2,X1))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_14]),c_0_14]) ).
cnf(c_0_34,plain,
ld(X1,mult(X1,X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_35,negated_conjecture,
( mult(X1,esk1_0) != unit
| mult(esk1_0,X1) != unit ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
mult(X1,mult(X1,rd(unit,X1))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_32]),c_0_14]),c_0_15]),c_0_33]),c_0_29]) ).
cnf(c_0_37,plain,
ld(X1,X1) = unit,
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_38,negated_conjecture,
mult(esk1_0,rd(unit,esk1_0)) != unit,
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_19])]) ).
cnf(c_0_39,plain,
mult(X1,rd(unit,X1)) = unit,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_36]),c_0_37]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38,c_0_39])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP700+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
% 0.16/0.33 % Computer : n002.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % 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 19:17:46 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.57/1.80 % Version : CSE_E---1.7
% 1.57/1.80 % Problem : theBenchmark.p
% 1.57/1.80 % SZS status Theorem for theBenchmark.p
% 1.57/1.80 % SZS output start CNFRefutation
% See solution above
% 1.57/1.80 % Total time : 1.370s
%------------------------------------------------------------------------------