%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP715+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 : n005.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 4.11s 3.27s
% Output : CNFRefutation 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 27 unt; 0 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 6 ~; 2 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f07,axiom,
! [X2,X3] : mult(X3,mult(X2,X2)) = mult(mult(X3,X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
fof(f06,axiom,
! [X1,X2,X3] : mult(mult(mult(X3,X2),X1),X2) = mult(X3,mult(mult(X2,X1),X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
fof(f09,axiom,
! [X3] : mult(unit,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
fof(f11,axiom,
mult(op_b,op_a) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
fof(f10,axiom,
mult(op_a,op_b) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
fof(f08,axiom,
! [X3] : mult(X3,unit) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
fof(goals,conjecture,
! [X4] :
( mult(mult(X4,op_a),op_b) = X4
& mult(mult(X4,op_b),op_a) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
fof(c_0_7,plain,
! [X36,X37] : mult(X37,mult(X36,X36)) = mult(mult(X37,X36),X36),
inference(variable_rename,[status(thm)],[f07]) ).
fof(c_0_8,plain,
! [X33,X34,X35] : mult(mult(mult(X35,X34),X33),X34) = mult(X35,mult(mult(X34,X33),X34)),
inference(variable_rename,[status(thm)],[f06]) ).
cnf(c_0_9,plain,
mult(X1,mult(X2,X2)) = mult(mult(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,plain,
mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(mult(X2,X3),X2)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_11,plain,
! [X39] : mult(unit,X39) = X39,
inference(variable_rename,[status(thm)],[f09]) ).
cnf(c_0_12,plain,
mult(mult(X1,mult(mult(X2,X3),X2)),X2) = mult(mult(mult(X1,X2),X3),mult(X2,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_13,plain,
mult(op_b,op_a) = unit,
inference(split_conjunct,[status(thm)],[f11]) ).
cnf(c_0_14,plain,
mult(unit,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
mult(op_a,op_b) = unit,
inference(split_conjunct,[status(thm)],[f10]) ).
fof(c_0_16,plain,
! [X38] : mult(X38,unit) = X38,
inference(variable_rename,[status(thm)],[f08]) ).
fof(c_0_17,negated_conjecture,
~ ! [X4] :
( mult(mult(X4,op_a),op_b) = X4
& mult(mult(X4,op_b),op_a) = X4 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_0_18,plain,
mult(mult(mult(X1,op_b),op_a),mult(op_b,op_b)) = mult(X1,mult(op_b,op_b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_9]) ).
cnf(c_0_19,plain,
mult(op_a,mult(op_b,op_b)) = op_b,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_15]),c_0_14]) ).
cnf(c_0_20,plain,
mult(X1,unit) = X1,
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,negated_conjecture,
( mult(mult(esk1_0,op_a),op_b) != esk1_0
| mult(mult(esk1_0,op_b),op_a) != esk1_0 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).
cnf(c_0_22,plain,
mult(mult(X1,mult(op_b,op_b)),op_a) = mult(X1,op_b),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_18]),c_0_19]),c_0_13]),c_0_20]) ).
cnf(c_0_23,plain,
mult(mult(mult(X1,mult(X2,X2)),X3),X2) = mult(mult(X1,X2),mult(mult(X2,X3),X2)),
inference(spm,[status(thm)],[c_0_10,c_0_9]) ).
cnf(c_0_24,negated_conjecture,
( mult(mult(esk1_0,op_a),op_b) != esk1_0
| mult(mult(esk1_0,op_b),op_a) != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,plain,
mult(mult(X1,op_a),op_b) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_22]),c_0_19]),c_0_13]),c_0_20]) ).
cnf(c_0_26,plain,
mult(mult(X1,mult(op_a,op_a)),op_b) = mult(X1,op_a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_19]),c_0_13]),c_0_20]) ).
cnf(c_0_27,plain,
mult(op_b,mult(op_a,op_a)) = op_a,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_13]),c_0_14]) ).
cnf(c_0_28,negated_conjecture,
mult(mult(esk1_0,op_b),op_a) != esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25])]) ).
cnf(c_0_29,plain,
mult(mult(X1,op_b),op_a) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_26]),c_0_27]),c_0_15]),c_0_20]) ).
cnf(c_0_30,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_29])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP715+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
% 0.16/0.33 % Computer : n005.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 19:03:15 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 4.11/3.27 % Version : CSE_E---1.7
% 4.11/3.27 % Problem : theBenchmark.p
% 4.11/3.27 % SZS status Theorem for theBenchmark.p
% 4.11/3.27 % SZS output start CNFRefutation
% See solution above
% 4.11/3.28 % Total time : 2.371s
%------------------------------------------------------------------------------