%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ANA034-10 : TPTP v9.2.1. Released v7.3.0.
% 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 : n021.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 1.59s 1.84s
% Output : CNFRefutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 18 RR)
% Number of literals : 45 ( 44 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 6 con; 0-4 aty)
% Number of variables : 59 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
cnf(ifeq_axiom_001,axiom,
ifeq(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,class_Orderings_Oorder(X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
ifeq(c_less(X1,X2,X3),true,ifeq(class_Orderings_Oorder(X3),true,c_lessequals(X1,X2,X3),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__cancel__semiring(X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__semiring(X1),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(c_0,X3,X1),true,c_lessequals(c_0,c_times(X2,X3,X1),X1),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
cnf(cls_Ring__and__Field_Omult__mono_0,axiom,
ifeq(c_lessequals(c_0,X1,X2),true,ifeq(c_lessequals(c_0,X3,X2),true,ifeq(c_lessequals(X4,X1,X2),true,ifeq(c_lessequals(X3,X5,X2),true,ifeq(class_Ring__and__Field_Opordered__semiring(X2),true,c_lessequals(c_times(X4,X3,X2),c_times(X1,X5,X2),X2),true),true),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
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) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
ifeq2(class_Ring__and__Field_Oordered__idom(X1),true,c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1),c_HOL_Oabs(c_times(X2,X3,X1),X1)) = c_HOL_Oabs(c_times(X2,X3,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
cnf(ifeq_axiom,axiom,
ifeq2(X1,X1,X2,X3) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
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) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
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) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(c_0_17,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_OrderedGroup_Olordered__ab__group__abs(X1),true) = true,
clsrel_Ring__and__Field_Oordered__idom_50 ).
cnf(c_0_18,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
tfree_tcs ).
cnf(c_0_19,axiom,
ifeq(X1,X1,X2,X3) = X2,
ifeq_axiom_001 ).
cnf(c_0_20,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,class_Orderings_Oorder(X1),true) = true,
clsrel_OrderedGroup_Olordered__ab__group__abs_17 ).
cnf(c_0_21,negated_conjecture,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_22,axiom,
ifeq(c_less(X1,X2,X3),true,ifeq(class_Orderings_Oorder(X3),true,c_lessequals(X1,X2,X3),true),true) = true,
cls_Orderings_Oorder__less__imp__le_0 ).
cnf(c_0_23,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
cls_conjecture_0 ).
cnf(c_0_24,negated_conjecture,
class_Orderings_Oorder(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_19]) ).
cnf(c_0_25,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__cancel__semiring(X1),true) = true,
clsrel_Ring__and__Field_Oordered__idom_40 ).
cnf(c_0_26,axiom,
ifeq(class_OrderedGroup_Olordered__ab__group__abs(X1),true,c_lessequals(c_0,c_HOL_Oabs(X2,X1),X1),true) = true,
cls_OrderedGroup_Oabs__ge__zero_0 ).
cnf(c_0_27,axiom,
ifeq(class_Ring__and__Field_Oordered__idom(X1),true,class_Ring__and__Field_Opordered__semiring(X1),true) = true,
clsrel_Ring__and__Field_Oordered__idom_42 ).
cnf(c_0_28,axiom,
ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(c_0,X3,X1),true,c_lessequals(c_0,c_times(X2,X3,X1),X1),true),true),true) = true,
cls_Ring__and__Field_Omult__nonneg__nonneg_0 ).
cnf(c_0_29,negated_conjecture,
c_lessequals(c_0,v_c,t_b) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_19]),c_0_24]),c_0_19]) ).
cnf(c_0_30,negated_conjecture,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_18]),c_0_19]) ).
cnf(c_0_31,axiom,
ifeq(c_lessequals(c_0,X1,X2),true,ifeq(c_lessequals(c_0,X3,X2),true,ifeq(c_lessequals(X4,X1,X2),true,ifeq(c_lessequals(X3,X5,X2),true,ifeq(class_Ring__and__Field_Opordered__semiring(X2),true,c_lessequals(c_times(X4,X3,X2),c_times(X1,X5,X2),X2),true),true),true),true),true) = true,
cls_Ring__and__Field_Omult__mono_0 ).
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) = true,
cls_conjecture_3 ).
cnf(c_0_33,negated_conjecture,
c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_19]) ).
cnf(c_0_34,negated_conjecture,
class_Ring__and__Field_Opordered__semiring(t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_18]),c_0_19]) ).
cnf(c_0_35,negated_conjecture,
ifeq(c_lessequals(c_0,X1,t_b),true,c_lessequals(c_0,c_times(v_c,X1,t_b),t_b),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]),c_0_19]),c_0_19]) ).
cnf(c_0_36,axiom,
ifeq2(class_Ring__and__Field_Oordered__idom(X1),true,c_times(c_HOL_Oabs(X2,X1),c_HOL_Oabs(X3,X1),X1),c_HOL_Oabs(c_times(X2,X3,X1),X1)) = c_HOL_Oabs(c_times(X2,X3,X1),X1),
cls_Ring__and__Field_Oabs__mult_0 ).
cnf(c_0_37,axiom,
ifeq2(X1,X1,X2,X3) = X2,
ifeq_axiom ).
cnf(c_0_38,negated_conjecture,
ifeq(c_lessequals(c_0,X1,t_b),true,ifeq(c_lessequals(X2,X1,t_b),true,c_lessequals(c_times(X2,c_HOL_Oabs(v_b(v_x),t_b),t_b),c_times(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b),t_b),true),true) = true,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34]),c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_39,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) = true,
cls_conjecture_2 ).
cnf(c_0_40,negated_conjecture,
c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X1,t_b),t_b),t_b) = true,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_33]),c_0_19]) ).
cnf(c_0_41,negated_conjecture,
c_times(c_HOL_Oabs(X1,t_b),c_HOL_Oabs(X2,t_b),t_b) = c_HOL_Oabs(c_times(X1,X2,t_b),t_b),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_18]),c_0_37]) ).
cnf(c_0_42,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_43,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) != true,
cls_conjecture_5 ).
cnf(c_0_44,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_41]),c_0_42]),c_0_19]),c_0_19]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA034-10 : TPTP v9.2.1. Released v7.3.0.
% 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
% 0.16/0.33 % Computer : n021.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 : Tue May 5 10:37:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.59/1.84 % Version : CSE_E---1.7
% 1.59/1.84 % Problem : theBenchmark.p
% 1.59/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.59/1.84 % SZS output start CNFRefutation
% See solution above
% 1.59/1.84 % Total time : 1.368s
%------------------------------------------------------------------------------