%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA031-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 09:31:21 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.28s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 60 ( 7 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 27 ~; 26 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 59 ( 59 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_b(X0),t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_f(v_x(X0)),t_b),c_HOL_Oabs(v_g(v_x(X0)),t_b),t_b),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__1_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_times(X1,X2,X0) = c_times(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omult__ac__2_0) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ class_Ring__and__Field_Opordered__semiring(X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0) ).
fof(f7,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Oab__semigroup__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f8,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Osemigroup__mult(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f9,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f10,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f12,plain,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( class_OrderedGroup_Osemigroup__mult(X0)
| c_times(c_times(X1,X2,X0),X3,X0) = c_times(X1,c_times(X2,X3,X0),X0) ),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f14,plain,
! [X2,X0,X1] :
( class_OrderedGroup_Oab__semigroup__mult(X0)
| c_times(X1,X2,X0) = c_times(X2,X1,X0) ),
inference(consistent_polarity_flipping,[],[f5]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_0,X3,X0)
| ~ c_lessequals(X1,X2,X0)
| class_Ring__and__Field_Opordered__semiring(X0)
| c_lessequals(c_times(X3,X1,X0),c_times(X3,X2,X0),X0) ),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f16,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Oab__semigroup__mult(X0) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f17,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Osemigroup__mult(X0) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f18,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f19,plain,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f20,plain,
~ class_OrderedGroup_Oab__semigroup__mult(t_b),
inference(resolution,[],[f16,f11]) ).
fof(f21,plain,
~ class_OrderedGroup_Osemigroup__mult(t_b),
inference(resolution,[],[f17,f11]) ).
fof(f22,plain,
~ class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolution,[],[f18,f11]) ).
fof(f23,plain,
~ class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f19,f11]) ).
fof(f24,plain,
! [X0,X1] : c_times(X0,X1,t_b) = c_times(X1,X0,t_b),
inference(resolution,[],[f14,f20]) ).
fof(f25,plain,
! [X2,X0,X1] : c_times(c_times(X0,X1,t_b),X2,t_b) = c_times(X0,c_times(X1,X2,t_b),t_b),
inference(resolution,[],[f13,f21]) ).
fof(f26,plain,
! [X0] : ~ c_lessequals(c_times(c_HOL_Oabs(v_b(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),c_times(X0,c_times(c_HOL_Oabs(v_g(v_x(X0)),t_b),c_HOL_Oabs(v_f(v_x(X0)),t_b),t_b),t_b),t_b),
inference(superposition,[],[f2,f24]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X0,X1,X2)
| class_Ring__and__Field_Opordered__semiring(X2)
| c_lessequals(c_times(c_HOL_Oabs(X3,X2),X0,X2),c_times(c_HOL_Oabs(X3,X2),X1,X2),X2)
| class_OrderedGroup_Olordered__ab__group__abs(X2) ),
inference(resolution,[],[f15,f12]) ).
fof(f29,plain,
! [X0,X1] :
( class_Ring__and__Field_Opordered__semiring(t_b)
| c_lessequals(c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(v_b(X1),t_b),t_b),c_times(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(resolution,[],[f28,f1]) ).
fof(f32,plain,
! [X0,X1] :
( c_lessequals(c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(v_b(X1),t_b),t_b),c_times(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),t_b)
| class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(forward_subsumption_resolution,[],[f29,f22]) ).
fof(f33,plain,
! [X0,X1] : c_lessequals(c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(v_b(X1),t_b),t_b),c_times(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_g(X1),t_b),t_b),t_b),t_b),
inference(forward_subsumption_resolution,[],[f32,f23]) ).
fof(f37,plain,
! [X2,X0,X1] : c_times(X0,c_times(X1,X2,t_b),t_b) = c_times(X1,c_times(X2,X0,t_b),t_b),
inference(superposition,[],[f25,f24]) ).
fof(f46,plain,
! [X0,X1] : c_lessequals(c_times(c_HOL_Oabs(v_b(X0),t_b),c_HOL_Oabs(X1,t_b),t_b),c_times(c_HOL_Oabs(X1,t_b),c_times(v_c,c_HOL_Oabs(v_g(X0),t_b),t_b),t_b),t_b),
inference(superposition,[],[f33,f24]) ).
fof(f288,plain,
! [X0,X1] : c_lessequals(c_times(c_HOL_Oabs(v_b(X0),t_b),c_HOL_Oabs(X1,t_b),t_b),c_times(v_c,c_times(c_HOL_Oabs(v_g(X0),t_b),c_HOL_Oabs(X1,t_b),t_b),t_b),t_b),
inference(forward_demodulation,[],[f46,f37]) ).
fof(f308,plain,
$false,
inference(resolution,[],[f26,f288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA031-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n011.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 20:32:16 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.28 % (3735667)Will run a generic schedule for satisfiability detection.
% 0.21/0.28 % (3735673)% WARNING: option uhcvi not known.
% 0.21/0.28 % (3735673)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1865250090:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.28 % (3735673) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3735667-3735673"...
% 0.21/0.28 % (3735672)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1804677159_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.28 % (3735673)...printing done.
% 0.21/0.28 % (3735673)Refutation found. Thanks to Tanya!
% 0.21/0.28 % SZS status Unsatisfiable for theBenchmark
% 0.21/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.28 % (3735673)------------------------------
% 0.21/0.28 % (3735673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.28 % (3735673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.28 % (3735673)CaDiCaL version: 2.1.3
% 0.21/0.28 % (3735673)Termination reason: Refutation
% 0.21/0.28 % (3735673)Time elapsed: 0.006 s
% 0.21/0.28 % (3735673)Peak memory usage: 11 MB
% 0.21/0.28 % (3735673)Instructions burned: 16 (million)
% 0.21/0.28 % (3735667)Success in time 0.036 s
% 0.21/0.28 % Vampire exiting
%------------------------------------------------------------------------------