%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA034-2 : 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 : n019.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 04:09:22 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 41 ( 15 unt; 0 nHn; 37 RR)
% Number of literals : 89 ( 4 equ; 53 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 49 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
cnf(cls_Ring__and__Field_Omult__mono_0,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X5,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
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/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_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_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(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(cls_conjecture_4,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( c_lessequals(c_0,c_times(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(cls_conjecture_5,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
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(c_0_15,axiom,
( c_lessequals(X2,X3,X1)
| ~ class_Orderings_Oorder(X1)
| ~ c_less(X2,X3,X1) ),
cls_Orderings_Oorder__less__imp__le_0 ).
cnf(c_0_16,negated_conjecture,
c_less(c_0,v_c,t_b),
cls_conjecture_0 ).
cnf(c_0_17,negated_conjecture,
( c_lessequals(c_0,v_c,t_b)
| ~ class_Orderings_Oorder(t_b) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,axiom,
( class_Orderings_Oorder(X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1) ),
clsrel_OrderedGroup_Olordered__ab__group__abs_17 ).
cnf(c_0_19,axiom,
( c_lessequals(c_times(X4,X2,X1),c_times(X5,X3,X1),X1)
| ~ class_Ring__and__Field_Opordered__semiring(X1)
| ~ c_lessequals(X2,X3,X1)
| ~ c_lessequals(X4,X5,X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X5,X1) ),
cls_Ring__and__Field_Omult__mono_0 ).
cnf(c_0_20,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_21,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_22,negated_conjecture,
( c_lessequals(c_0,v_c,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,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_24,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
tfree_tcs ).
cnf(c_0_25,plain,
( c_lessequals(c_HOL_Oabs(c_times(X1,X2,X3),X3),c_times(X4,X5,X3),X3)
| ~ c_lessequals(c_0,c_HOL_Oabs(X2,X3),X3)
| ~ c_lessequals(c_HOL_Oabs(X1,X3),X4,X3)
| ~ c_lessequals(c_HOL_Oabs(X2,X3),X5,X3)
| ~ c_lessequals(c_0,X4,X3)
| ~ class_Ring__and__Field_Oordered__idom(X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_26,negated_conjecture,
c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b) = c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
cls_conjecture_4 ).
cnf(c_0_27,axiom,
( c_lessequals(c_0,c_times(X3,X2,X1),X1)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ c_lessequals(c_0,X2,X1)
| ~ c_lessequals(c_0,X3,X1) ),
cls_Ring__and__Field_Omult__nonneg__nonneg_0 ).
cnf(c_0_28,negated_conjecture,
c_lessequals(c_0,v_c,t_b),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24])]) ).
cnf(c_0_29,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(c_times(v_a(v_x),v_b(v_x),t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b),
cls_conjecture_5 ).
cnf(c_0_30,negated_conjecture,
( c_lessequals(c_HOL_Oabs(c_times(X1,X2,t_b),t_b),c_times(c_times(v_c,v_ca,t_b),c_HOL_Oabs(c_times(v_f(v_x),v_g(v_x),t_b),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X1,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X2,t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X2,t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_24])]) ).
cnf(c_0_31,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_a(v_x),t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),
cls_conjecture_2 ).
cnf(c_0_32,negated_conjecture,
c_lessequals(c_HOL_Oabs(v_b(v_x),t_b),c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),
cls_conjecture_3 ).
cnf(c_0_33,negated_conjecture,
( c_lessequals(c_0,c_times(v_c,X1,t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ c_lessequals(c_0,X1,t_b) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ),
clsrel_Ring__and__Field_Oordered__idom_40 ).
cnf(c_0_35,negated_conjecture,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_32])]) ).
cnf(c_0_36,negated_conjecture,
( c_lessequals(c_0,c_times(v_c,X1,t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_24])]) ).
cnf(c_0_37,negated_conjecture,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,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_39,negated_conjecture,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_38]) ).
cnf(c_0_40,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_23]),c_0_24])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA034-2 : 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 : n019.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 10:36:44 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------