%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA014-2 : TPTP v9.2.1. Released v3.2.0.
% 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 : n013.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 04:09:17 PM UTC 2026
% Result : Unsatisfiable 1.20s 1.69s
% Output : CNFRefutation 1.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of clauses : 40 ( 9 unt; 7 nHn; 22 RR)
% Number of literals : 76 ( 25 equ; 38 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
( c_times(c_1,X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
cnf(clsrel_Ring__and__Field_Ofield_12,axiom,
( class_OrderedGroup_Omonoid__mult(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_12) ).
cnf(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( X2 = c_0
| c_times(c_HOL_Oinverse(X2,X1),X2,X1) = c_1
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_0) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ofield_21) ).
cnf(cls_conjecture_0,negated_conjecture,
v_c != c_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
( class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_34) ).
cnf(clsrel_Ring__and__Field_Oordered__field_58,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__field_58) ).
cnf(c_0_13,axiom,
( c_times(c_1,X2,X1) = X2
| ~ class_OrderedGroup_Omonoid__mult(X1) ),
cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0 ).
cnf(c_0_14,axiom,
( class_OrderedGroup_Omonoid__mult(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
clsrel_Ring__and__Field_Ofield_12 ).
cnf(c_0_15,axiom,
( X2 = c_0
| c_times(c_HOL_Oinverse(X2,X1),X2,X1) = c_1
| ~ class_Ring__and__Field_Ofield(X1) ),
cls_Ring__and__Field_Ofield__class_Oaxioms__1_0 ).
cnf(c_0_16,axiom,
( class_Ring__and__Field_Ofield(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
clsrel_Ring__and__Field_Oordered__field_0 ).
cnf(c_0_17,plain,
( c_times(c_1,X1,X2) = X1
| ~ class_Ring__and__Field_Ofield(X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
( c_times(c_HOL_Oinverse(X1,X2),X1,X2) = c_1
| X1 = c_0
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
class_Ring__and__Field_Oordered__field(t_a),
tfree_tcs ).
cnf(c_0_20,plain,
( c_times(c_1,X1,X2) = X1
| ~ class_Ring__and__Field_Oordered__field(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,axiom,
( c_times(c_times(X2,X3,X1),X4,X1) = c_times(X2,c_times(X3,X4,X1),X1)
| ~ class_OrderedGroup_Osemigroup__mult(X1) ),
cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0 ).
cnf(c_0_22,negated_conjecture,
( c_times(c_HOL_Oinverse(X1,t_a),X1,t_a) = c_1
| X1 = c_0 ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
c_times(c_1,X1,t_a) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_19]) ).
cnf(c_0_24,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_times(c_HOL_Oabs(v_c,t_a),c_HOL_Oabs(v_f(v_x(X1)),t_a),t_a),t_a),t_a),
cls_conjecture_1 ).
cnf(c_0_25,axiom,
( c_HOL_Oabs(c_times(X2,X3,X1),X1) = c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
cls_Ring__and__Field_Oabs__mult_0 ).
cnf(c_0_26,negated_conjecture,
( c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X2,t_a),t_a) = X2
| X1 = c_0
| ~ class_OrderedGroup_Osemigroup__mult(t_a) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_27,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Ofield(X1) ),
clsrel_Ring__and__Field_Ofield_21 ).
cnf(c_0_28,negated_conjecture,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_x(X1)),t_a),c_times(X1,c_HOL_Oabs(c_times(v_c,v_f(v_x(X1)),t_a),t_a),t_a),t_a) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,negated_conjecture,
( c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X2,t_a),t_a) = X2
| X1 = c_0
| ~ class_Ring__and__Field_Ofield(t_a) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,negated_conjecture,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),c_HOL_Oabs(c_times(X1,c_times(v_c,v_f(v_x(c_HOL_Oabs(X1,t_a))),t_a),t_a),t_a),t_a) ),
inference(spm,[status(thm)],[c_0_28,c_0_25]) ).
cnf(c_0_31,negated_conjecture,
( c_times(c_HOL_Oinverse(X1,t_a),c_times(X1,X2,t_a),t_a) = X2
| X1 = c_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_16]),c_0_19])]) ).
cnf(c_0_32,negated_conjecture,
v_c != c_0,
cls_conjecture_0 ).
cnf(c_0_33,negated_conjecture,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ c_lessequals(c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),c_HOL_Oabs(v_f(v_x(c_HOL_Oabs(c_HOL_Oinverse(v_c,t_a),t_a))),t_a),t_a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_34,axiom,
( c_lessequals(X2,X2,X1)
| ~ class_Orderings_Oorder(X1) ),
cls_Orderings_Oorder__class_Oaxioms__1_0 ).
cnf(c_0_35,negated_conjecture,
( ~ class_Ring__and__Field_Oordered__idom(t_a)
| ~ class_Orderings_Oorder(t_a) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_36,axiom,
( class_Ring__and__Field_Oordered__idom(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
clsrel_Ring__and__Field_Oordered__field_34 ).
cnf(c_0_37,negated_conjecture,
~ class_Orderings_Oorder(t_a),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19])]) ).
cnf(c_0_38,axiom,
( class_Orderings_Oorder(X1)
| ~ class_Ring__and__Field_Oordered__field(X1) ),
clsrel_Ring__and__Field_Oordered__field_58 ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ANA014-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.13/0.30 % Computer : n013.cluster.edu
% 0.13/0.30 % Model : x86_64 x86_64
% 0.13/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.30 % Memory : 8042.1875MB
% 0.13/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.30 % CPULimit : 300
% 0.13/0.30 % WCLimit : 300
% 0.13/0.30 % DateTime : Tue May 5 10:35:11 EDT 2026
% 0.13/0.30 % CPUTime :
% 0.13/0.31 % start to proof: theBenchmark
% 1.20/1.69 % Version : CSE_E---1.7
% 1.20/1.69 % Problem : theBenchmark.p
% 1.20/1.69 % SZS status Unsatisfiable for theBenchmark.p
% 1.20/1.69 % SZS output start CNFRefutation
% See solution above
% 1.20/1.69 % Total time : 1.370s
%------------------------------------------------------------------------------