%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 : Tue Sep 29 09:31:19 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.26s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 52 unt; 0 def)
% Number of atoms : 52 ( 51 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 4 con; 0-4 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] : ifeq2(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
fof(f2,axiom,
! [X2,X0,X1] : ifeq(X0,X0,X1,X2) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
fof(f3,axiom,
! [X0,X1] : ifeq2(class_OrderedGroup_Ocomm__monoid__add(X0),true,c_plus(c_0,X1,X0),X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(X1,c_minus(X2,X3,X0),X0),true,c_lessequals(c_plus(X1,X3,X0),X2,X0),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
fof(f5,plain,
! [X2,X3,X0,X1] : true = ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(X1,c_minus(X2,X3,X0),X0),true,c_lessequals(c_plus(X1,X3,X0),X2,X0),true),true),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X2,X3,X0,X1] : ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(c_plus(X1,X2,X0),X3,X0),true,c_lessequals(X1,c_minus(X3,X2,X0),X0),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f7,plain,
! [X2,X3,X0,X1] : true = ifeq(class_OrderedGroup_Opordered__ab__group__add(X0),true,ifeq(c_lessequals(c_plus(X1,X2,X0),X3,X0),true,c_lessequals(X1,c_minus(X3,X2,X0),X0),true),true),
inference(reorient_equations,[],[f6]) ).
fof(f8,axiom,
! [X2,X3,X0,X1] : ifeq(class_Orderings_Oorder(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X2,X3,X0),true,c_lessequals(X1,X3,X0),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f9,plain,
! [X2,X3,X0,X1] : true = ifeq(class_Orderings_Oorder(X0),true,ifeq(c_lessequals(X1,X2,X0),true,ifeq(c_lessequals(X2,X3,X0),true,c_lessequals(X1,X3,X0),true),true),true),
inference(reorient_equations,[],[f8]) ).
fof(f10,negated_conjecture,
c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f11,plain,
true = c_lessequals(c_0,c_minus(v_k(v_x),v_g(v_x),t_b),t_b),
inference(reorient_equations,[],[f10]) ).
fof(f12,negated_conjecture,
c_lessequals(v_k(v_x),v_f(v_x),t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f13,plain,
true = c_lessequals(v_k(v_x),v_f(v_x),t_b),
inference(reorient_equations,[],[f12]) ).
fof(f14,negated_conjecture,
c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f15,plain,
true != c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0] : ifeq(class_Orderings_Olinorder(X0),true,class_Orderings_Oorder(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f17,plain,
! [X0] : true = ifeq(class_Orderings_Olinorder(X0),true,class_Orderings_Oorder(X0),true),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f19,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Ocomm__monoid__add(X0),true),
inference(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Olinorder(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f21,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_Orderings_Olinorder(X0),true),
inference(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0] : ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f23,plain,
! [X0] : true = ifeq(class_Ring__and__Field_Oordered__idom(X0),true,class_OrderedGroup_Opordered__ab__group__add(X0),true),
inference(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f25,plain,
true = class_Ring__and__Field_Oordered__idom(t_b),
inference(reorient_equations,[],[f24]) ).
fof(f26,plain,
true = ifeq(true,true,class_OrderedGroup_Ocomm__monoid__add(t_b),true),
inference(superposition,[],[f19,f25]) ).
fof(f27,plain,
true = class_OrderedGroup_Ocomm__monoid__add(t_b),
inference(forward_demodulation,[],[f26,f2]) ).
fof(f30,plain,
true = ifeq(true,true,class_Orderings_Olinorder(t_b),true),
inference(superposition,[],[f21,f25]) ).
fof(f31,plain,
true = class_Orderings_Olinorder(t_b),
inference(forward_demodulation,[],[f30,f2]) ).
fof(f33,plain,
true = ifeq(true,true,class_Orderings_Oorder(t_b),true),
inference(superposition,[],[f17,f31]) ).
fof(f34,plain,
true = class_Orderings_Oorder(t_b),
inference(forward_demodulation,[],[f33,f2]) ).
fof(f36,plain,
true = ifeq(true,true,class_OrderedGroup_Opordered__ab__group__add(t_b),true),
inference(superposition,[],[f23,f25]) ).
fof(f37,plain,
true = class_OrderedGroup_Opordered__ab__group__add(t_b),
inference(forward_demodulation,[],[f36,f2]) ).
fof(f40,plain,
! [X0] : ifeq2(true,true,c_plus(c_0,X0,t_b),X0) = X0,
inference(superposition,[],[f3,f27]) ).
fof(f41,plain,
! [X0] : c_plus(c_0,X0,t_b) = X0,
inference(forward_demodulation,[],[f40,f1]) ).
fof(f45,plain,
true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(true,true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),true),
inference(superposition,[],[f5,f11]) ).
fof(f46,plain,
true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,c_lessequals(c_plus(c_0,v_g(v_x),t_b),v_k(v_x),t_b),true),
inference(forward_demodulation,[],[f45,f2]) ).
fof(f48,plain,
true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true),
inference(forward_demodulation,[],[f46,f41]) ).
fof(f49,plain,
true = ifeq(true,true,c_lessequals(v_g(v_x),v_k(v_x),t_b),true),
inference(forward_demodulation,[],[f48,f37]) ).
fof(f50,plain,
true = c_lessequals(v_g(v_x),v_k(v_x),t_b),
inference(forward_demodulation,[],[f49,f2]) ).
fof(f57,plain,
! [X0,X1] : true = ifeq(class_OrderedGroup_Opordered__ab__group__add(t_b),true,ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_0,c_minus(X1,X0,t_b),t_b),true),true),
inference(superposition,[],[f7,f41]) ).
fof(f60,plain,
! [X0,X1] : true = ifeq(true,true,ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_0,c_minus(X1,X0,t_b),t_b),true),true),
inference(forward_demodulation,[],[f57,f37]) ).
fof(f63,plain,
! [X0,X1] : true = ifeq(c_lessequals(X0,X1,t_b),true,c_lessequals(c_0,c_minus(X1,X0,t_b),t_b),true),
inference(forward_demodulation,[],[f60,f2]) ).
fof(f70,plain,
! [X0] : true = ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X0,v_k(v_x),t_b),true,ifeq(true,true,c_lessequals(X0,v_f(v_x),t_b),true),true),true),
inference(superposition,[],[f9,f13]) ).
fof(f81,plain,
! [X0] : true = ifeq(class_Orderings_Oorder(t_b),true,ifeq(c_lessequals(X0,v_k(v_x),t_b),true,c_lessequals(X0,v_f(v_x),t_b),true),true),
inference(forward_demodulation,[],[f70,f2]) ).
fof(f91,plain,
! [X0] : true = ifeq(true,true,ifeq(c_lessequals(X0,v_k(v_x),t_b),true,c_lessequals(X0,v_f(v_x),t_b),true),true),
inference(forward_demodulation,[],[f81,f34]) ).
fof(f97,plain,
! [X0] : true = ifeq(c_lessequals(X0,v_k(v_x),t_b),true,c_lessequals(X0,v_f(v_x),t_b),true),
inference(forward_demodulation,[],[f91,f2]) ).
fof(f101,plain,
true = ifeq(true,true,c_lessequals(v_g(v_x),v_f(v_x),t_b),true),
inference(superposition,[],[f97,f50]) ).
fof(f103,plain,
true = c_lessequals(v_g(v_x),v_f(v_x),t_b),
inference(forward_demodulation,[],[f101,f2]) ).
fof(f192,plain,
true = ifeq(true,true,c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),true),
inference(superposition,[],[f63,f103]) ).
fof(f195,plain,
true = c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
inference(forward_demodulation,[],[f192,f2]) ).
fof(f199,plain,
$false,
inference(forward_subsumption_resolution,[],[f195,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA023-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Mon Sep 28 20:29:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.26 % (197267)Will run a generic schedule for satisfiability detection.
% 0.07/0.26 % (197276)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2882461789:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.26 % (197273)% WARNING: option uhcvi not known.
% 0.07/0.26 % (197276) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-197267-197276"...
% 0.07/0.26 % (197276)...printing done.
% 0.07/0.26 % (197276)Refutation found. Thanks to Tanya!
% 0.07/0.26 % SZS status Unsatisfiable for theBenchmark
% 0.07/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.26 % (197276)------------------------------
% 0.07/0.26 % (197276)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.26 % (197276)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.26 % (197276)CaDiCaL version: 2.1.3
% 0.07/0.26 % (197276)Termination reason: Refutation
% 0.07/0.26 % (197276)Time elapsed: 0.005 s
% 0.07/0.26 % (197276)Peak memory usage: 11 MB
% 0.07/0.26 % (197276)Instructions burned: 13 (million)
% 0.07/0.26 % (197267)Success in time 0.038 s
% 0.07/0.26 % Vampire exiting
%------------------------------------------------------------------------------