%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA031-2 : TPTP v9.2.1. Released v3.2.0.
% 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 : 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 04:09:21 PM UTC 2026
% Result : Unsatisfiable 9.05s 6.11s
% Output : CNFRefutation 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 10 unt; 0 nHn; 23 RR)
% Number of literals : 71 ( 7 equ; 45 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 55 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Omult__ac__2_0,axiom,
( c_times(X2,X3,X1) = c_times(X3,X2,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
( class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_0,X4,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
cnf(cls_OrderedGroup_Omult__ac__1_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/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X1)),t_b),c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_f(v_x(X1)),t_b),c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(c_0_11,axiom,
( c_times(X2,X3,X1) = c_times(X3,X2,X1)
| ~ class_OrderedGroup_Oab__semigroup__mult(X1) ),
cls_OrderedGroup_Omult__ac__2_0 ).
cnf(c_0_12,axiom,
( class_OrderedGroup_Oab__semigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_17 ).
cnf(c_0_13,plain,
( c_times(X1,X2,X3) = c_times(X2,X1,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_14,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_15,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X4,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(c_0,X4,X1) ),
cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0 ).
cnf(c_0_16,negated_conjecture,
c_times(X1,X2,t_b) = c_times(X2,X1,t_b),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,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_Omult__ac__1_0 ).
cnf(c_0_18,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X1)),t_b),c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_f(v_x(X1)),t_b),c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b),t_b),
cls_conjecture_1 ).
cnf(c_0_19,negated_conjecture,
( c_lessequals(c_times(X1,X2,t_b),c_times(X2,X3,t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ c_lessequals(c_0,X2,t_b)
| ~ c_lessequals(X1,X3,t_b) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( c_times(X1,c_times(X2,X3,t_b),t_b) = c_times(X2,c_times(X3,X1,t_b),t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X1)),t_b),c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),c_times(X1,c_times(c_HOL_Oabs(v_g(v_x(X1)),t_b),c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b),t_b),t_b),
inference(rw,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_22,negated_conjecture,
( c_lessequals(c_times(X1,X2,t_b),c_times(X3,c_times(X4,X2,t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(X1,c_times(X3,X4,t_b),t_b)
| ~ c_lessequals(c_0,X2,t_b) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(c_HOL_Oabs(v_b(v_x(X1)),t_b),c_times(X1,c_HOL_Oabs(v_g(v_x(X1)),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(X1)),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_24,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(X1),t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),
cls_conjecture_0 ).
cnf(c_0_25,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x(v_c)),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,axiom,
( c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
cls_OrderedGroup_Oabs__ge__zero_0 ).
cnf(c_0_27,negated_conjecture,
( ~ class_Ring__and__Field_Opordered__semiring(t_b)
| ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,axiom,
( class_Ring__and__Field_Opordered__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_42 ).
cnf(c_0_29,negated_conjecture,
( ~ class_OrderedGroup_Osemigroup__mult(t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_14])]) ).
cnf(c_0_30,axiom,
( class_OrderedGroup_Osemigroup__mult(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_21 ).
cnf(c_0_31,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_14])]) ).
cnf(c_0_32,axiom,
( class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_50 ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_14])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA031-2 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:36:38 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 9.05/6.11 % Version : CSE_E---1.7
% 9.05/6.11 % Problem : theBenchmark.p
% 9.05/6.11 % SZS status Unsatisfiable for theBenchmark.p
% 9.05/6.11 % SZS output start CNFRefutation
% See solution above
% 9.15/6.15 % Total time : 4.371s
%------------------------------------------------------------------------------