%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV680-1 : TPTP v9.2.1. Released v4.1.0.
% 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 : 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 05:27:12 PM UTC 2026
% Result : Unsatisfiable 10.77s 7.22s
% Output : CNFRefutation 10.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 12 unt; 2 nHn; 18 RR)
% Number of literals : 42 ( 23 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-3 aty)
% Number of variables : 34 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_nat__mult__commute_0,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
cnf(cls_nonzero__power__divide_0,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_class__semiring_Opwr__pwr_0,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).
cnf(clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1) ).
cnf(cls_field__power__not__zero_0,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).
cnf(cls_conjecture_0,negated_conjecture,
v_a != c_HOL_Ozero__class_Ozero(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors) ).
cnf(c_0_9,negated_conjecture,
c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_k,v_i,tc_nat),t_a),t_a) != c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a),
cls_conjecture_1 ).
cnf(c_0_10,axiom,
c_HOL_Otimes__class_Otimes(X1,X2,tc_nat) = c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),
cls_nat__mult__commute_0 ).
cnf(c_0_11,negated_conjecture,
c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,v_j,t_a),c_Power_Opower__class_Opower(v_a,v_k,t_a),t_a),v_i,t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,axiom,
( c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(X2,X3,X1),X4,X1) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(X2,X4,X1),c_Power_Opower__class_Opower(X3,X4,X1),X1)
| X3 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_nonzero__power__divide_0 ).
cnf(c_0_13,negated_conjecture,
class_Ring__and__Field_Ofield(t_a),
tfree_tcs ).
cnf(c_0_14,axiom,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X2,X3,X1),X4,X1) = c_Power_Opower__class_Opower(X2,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X1) ),
cls_class__semiring_Opwr__pwr_0 ).
cnf(c_0_15,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
clsrel_Ring__and__Field_Ofield_Ring__and__Field_Ocomm__semiring__1 ).
cnf(c_0_16,negated_conjecture,
( c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_k,t_a),v_i,t_a),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13])]) ).
cnf(c_0_17,plain,
( c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(X1,X2,X3),X4,X3) = c_Power_Opower__class_Opower(X1,c_HOL_Otimes__class_Otimes(X2,X4,tc_nat),X3)
| ~ class_Ring__and__Field_Ofield(X3) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
( c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(v_a,v_j,t_a),v_i,t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a) != c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),t_a),c_Power_Opower__class_Opower(v_a,c_HOL_Otimes__class_Otimes(v_i,v_k,tc_nat),t_a),t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_10]),c_0_13])]) ).
cnf(c_0_19,axiom,
( X2 = c_HOL_Ozero__class_Ozero(X1)
| ~ class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| c_Power_Opower__class_Opower(X2,X3,X1) != c_HOL_Ozero__class_Ozero(X1) ),
cls_field__power__not__zero_0 ).
cnf(c_0_20,negated_conjecture,
c_Power_Opower__class_Opower(v_a,v_k,t_a) = c_HOL_Ozero__class_Ozero(t_a),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_17]),c_0_13])]),c_0_10]) ).
cnf(c_0_21,negated_conjecture,
v_a != c_HOL_Ozero__class_Ozero(t_a),
cls_conjecture_0 ).
cnf(c_0_22,negated_conjecture,
~ class_Ring__and__Field_Oring__1__no__zero__divisors(t_a),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_23,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
clsrel_Ring__and__Field_Ofield_Ring__and__Field_Oring__1__no__zero__divisors ).
cnf(c_0_24,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_13])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV680-1 : TPTP v9.2.1. Released v4.1.0.
% 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
% 0.14/0.33 % 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 : Tue May 5 05:47:53 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 10.77/7.22 % Version : CSE_E---1.7
% 10.77/7.22 % Problem : theBenchmark.p
% 10.77/7.22 % SZS status Unsatisfiable for theBenchmark.p
% 10.77/7.22 % SZS output start CNFRefutation
% See solution above
% 10.77/7.26 % Total time : 5.432s
%------------------------------------------------------------------------------