%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:02:17 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 17
% Syntax : Number of formulae : 69 ( 69 unt; 0 def)
% Number of atoms : 69 ( 68 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 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 : 76 ( 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq2(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [T_a,V_a,V_b] : ifeq2(class_Ring__and__Field_Oordered__idom(T_a),true,c_times(c_HOL_Oabs(V_a,T_a),c_HOL_Oabs(V_b,T_a),T_a),c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a)) = c_HOL_Oabs(c_times(V_a,V_b,T_a),T_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [V_b,T_a,V_c,V_a,V_d] : ifeq(c_lessequals(c_0,V_b,T_a),true,ifeq(c_lessequals(c_0,V_c,T_a),true,ifeq(c_lessequals(V_a,V_b,T_a),true,ifeq(c_lessequals(V_c,V_d,T_a),true,ifeq(class_Ring__and__Field_Opordered__semiring(T_a),true,c_lessequals(c_times(V_a,V_c,T_a),c_times(V_b,V_d,T_a),T_a),true),true),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [T_a,V_a,V_b] : ifeq(class_Ring__and__Field_Opordered__cancel__semiring(T_a),true,ifeq(c_lessequals(c_0,V_a,T_a),true,ifeq(c_lessequals(c_0,V_b,T_a),true,c_lessequals(c_0,c_times(V_a,V_b,T_a),T_a),true),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [V_x,V_y,T_a] : ifeq(c_less(V_x,V_y,T_a),true,ifeq(class_Orderings_Oorder(T_a),true,c_lessequals(V_x,V_y,T_a),true),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [T_a,V_a] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(T_a),true,c_lessequals(c_0,c_HOL_Oabs(V_a,T_a),T_a),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
c_less(c_0,v_c,t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,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/sandbox/benchmark/theBenchmark.p') ).
fof(f10,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/sandbox/benchmark/theBenchmark.p') ).
fof(f11,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') ).
fof(f12,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/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [T] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(T),true,class_Orderings_Oorder(T),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [T] : ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__cancel__semiring(T),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [T] : ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_Ring__and__Field_Opordered__semiring(T),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [T] : ifeq(class_Ring__and__Field_Oordered__idom(T),true,class_OrderedGroup_Olordered__ab__group__abs(T),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,plain,
! [X0,X1,X2] : ifeq2(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f19,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
! [X0,X1,X2] : ifeq2(class_Ring__and__Field_Oordered__idom(X0),true,c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0),c_HOL_Oabs(c_times(X1,X2,X0),X0)) = c_HOL_Oabs(c_times(X1,X2,X0),X0),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [X0,X1,X2,X3,X4] : ifeq(c_lessequals(c_0,X0,X1),true,ifeq(c_lessequals(c_0,X2,X1),true,ifeq(c_lessequals(X3,X0,X1),true,ifeq(c_lessequals(X2,X4,X1),true,ifeq(class_Ring__and__Field_Opordered__semiring(X1),true,c_lessequals(c_times(X3,X2,X1),c_times(X0,X4,X1),X1),true),true),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f22,plain,
! [X0,X1,X2] : ifeq(class_Ring__and__Field_Opordered__cancel__semiring(X0),true,ifeq(c_lessequals(c_0,X1,X0),true,ifeq(c_lessequals(c_0,X2,X0),true,c_lessequals(c_0,c_times(X1,X2,X0),X0),true),true),true) = true,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f23,plain,
! [X0,X1,X2] : ifeq(c_less(X0,X1,X2),true,ifeq(class_Orderings_Oorder(X2),true,c_lessequals(X0,X1,X2),true),true) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f24,plain,
! [X0,X1] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0),true) = true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
c_less(c_0,v_c,t_b) = true,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
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,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
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,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f28,plain,
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),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
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,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
class_Ring__and__Field_Oordered__idom(t_b) = true,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f31,plain,
! [X0] : ifeq(class_OrderedGroup_Olordered__ab__group__abs(X0),true,class_Orderings_Oorder(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f32,plain,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__cancel__semiring(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f33,plain,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Ring__and__Field_Opordered__semiring(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f34,plain,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Olordered__ab__group__abs(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f47,plain,
ifeq(true,true,ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true),true) = true,
inference(paramodulation,[status(thm)],[f25,f23]) ).
fof(f50,plain,
ifeq(class_Orderings_Oorder(t_b),true,c_lessequals(c_0,v_c,t_b),true) = true,
inference(forward_demodulation,[status(thm)],[f19,f47]) ).
fof(f53,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__cancel__semiring(t_b),true) = true,
inference(paramodulation,[status(thm)],[f30,f32]) ).
fof(f54,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f53]) ).
fof(f57,plain,
ifeq(true,true,class_Ring__and__Field_Opordered__semiring(t_b),true) = true,
inference(paramodulation,[status(thm)],[f30,f33]) ).
fof(f58,plain,
class_Ring__and__Field_Opordered__semiring(t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f57]) ).
fof(f61,plain,
! [X0,X1] : ifeq2(true,true,c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),c_HOL_Oabs(c_times(X0,X1,t_b),t_b)) = c_HOL_Oabs(c_times(X0,X1,t_b),t_b),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f63,plain,
! [X0,X1] : c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b) = c_HOL_Oabs(c_times(X0,X1,t_b),t_b),
inference(forward_demodulation,[status(thm)],[f18,f61]) ).
fof(f66,plain,
ifeq(true,true,class_OrderedGroup_Olordered__ab__group__abs(t_b),true) = true,
inference(paramodulation,[status(thm)],[f30,f34]) ).
fof(f67,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f66]) ).
fof(f69,plain,
ifeq(true,true,class_Orderings_Oorder(t_b),true) = true,
inference(paramodulation,[status(thm)],[f67,f31]) ).
fof(f73,plain,
ifeq(true,true,c_lessequals(c_0,v_c,t_b),true) = true,
inference(backward_demodulation,[status(thm)],[f74,f50]) ).
fof(f74,plain,
class_Orderings_Oorder(t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f69]) ).
fof(f77,plain,
c_lessequals(c_0,v_c,t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f73]) ).
fof(f86,plain,
! [X0] : ifeq(true,true,c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b),true) = true,
inference(paramodulation,[status(thm)],[f67,f24]) ).
fof(f87,plain,
! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,t_b),t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f86]) ).
fof(f107,plain,
! [X0] : ifeq(class_Ring__and__Field_Opordered__cancel__semiring(t_b),true,ifeq(true,true,ifeq(c_lessequals(c_0,X0,t_b),true,c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),true),true),true) = true,
inference(paramodulation,[status(thm)],[f77,f22]) ).
fof(f116,plain,
! [X0] : ifeq(true,true,ifeq(true,true,ifeq(c_lessequals(c_0,X0,t_b),true,c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f54,f107]) ).
fof(f117,plain,
! [X0] : ifeq(true,true,ifeq(c_lessequals(c_0,X0,t_b),true,c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),true),true) = true,
inference(forward_demodulation,[status(thm)],[f19,f116]) ).
fof(f118,plain,
! [X0] : ifeq(c_lessequals(c_0,X0,t_b),true,c_lessequals(c_0,c_times(v_c,X0,t_b),t_b),true) = true,
inference(forward_demodulation,[status(thm)],[f19,f117]) ).
fof(f133,plain,
! [X0] : ifeq(true,true,c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X0,t_b),t_b),t_b),true) = true,
inference(paramodulation,[status(thm)],[f87,f118]) ).
fof(f137,plain,
! [X0] : c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(X0,t_b),t_b),t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f133]) ).
fof(f200,plain,
! [X0,X1] : ifeq(c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b),true,ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(true,true,ifeq(c_lessequals(X0,X1,t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),X0,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),X1,t_b),t_b),true),true),true),true),true) = true,
inference(paramodulation,[status(thm)],[f26,f21]) ).
fof(f259,plain,
! [X0,X1] : ifeq(true,true,ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(true,true,ifeq(c_lessequals(X0,X1,t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),X0,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),X1,t_b),t_b),true),true),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f137,f200]) ).
fof(f260,plain,
! [X0,X1] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(true,true,ifeq(c_lessequals(X0,X1,t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),X0,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),X1,t_b),t_b),true),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f19,f259]) ).
fof(f261,plain,
! [X0,X1] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(X0,X1,t_b),true,ifeq(class_Ring__and__Field_Opordered__semiring(t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),X0,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),X1,t_b),t_b),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f19,f260]) ).
fof(f262,plain,
! [X0,X1] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(X0,X1,t_b),true,ifeq(true,true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),X0,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),X1,t_b),t_b),true),true),true) = true,
inference(forward_demodulation,[status(thm)],[f58,f261]) ).
fof(f263,plain,
! [X0,X1] : ifeq(c_lessequals(c_0,X0,t_b),true,ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),X0,t_b),c_times(c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),X1,t_b),t_b),true),true) = true,
inference(forward_demodulation,[status(thm)],[f19,f262]) ).
fof(f451,plain,
ifeq(c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b),true,ifeq(true,true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),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),t_b),true),true) = true,
inference(paramodulation,[status(thm)],[f27,f263]) ).
fof(f468,plain,
ifeq(true,true,ifeq(true,true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),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),t_b),true),true) = true,
inference(forward_demodulation,[status(thm)],[f87,f451]) ).
fof(f469,plain,
ifeq(true,true,c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),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),t_b),true) = true,
inference(forward_demodulation,[status(thm)],[f19,f468]) ).
fof(f470,plain,
c_lessequals(c_times(c_HOL_Oabs(v_a(v_x),t_b),c_HOL_Oabs(v_b(v_x),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),t_b) = true,
inference(forward_demodulation,[status(thm)],[f19,f469]) ).
fof(f471,plain,
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,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),t_b) = true,
inference(forward_demodulation,[status(thm)],[f63,f470]) ).
fof(f472,plain,
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,
inference(forward_demodulation,[status(thm)],[f28,f471]) ).
fof(f473,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f472,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA034-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n007.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 13:23:21 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.48 % Drodi V4.1.1
% 0.17/0.50 % Refutation found
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.53 % Elapsed time: 0.062809 seconds
% 0.17/0.53 % CPU time: 0.150909 seconds
% 0.17/0.53 % Total memory used: 8.625 MB
% 0.17/0.53 % Net memory used: 8.559 MB
%------------------------------------------------------------------------------