%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 09:30:58 AM UTC 2026
% Result : Unsatisfiable 0.21s 1.16s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 17
% Syntax : Number of formulae : 50 ( 19 unt; 2 def)
% Number of atoms : 108 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 61 ~; 56 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 30 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_HOL_Oabs(c_times(X1,X2,X0),X0) = c_times(c_HOL_Oabs(X1,X0),c_HOL_Oabs(X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__mult_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4] :
( c_lessequals(c_times(X3,X1,X0),c_times(X4,X2,X0),X0)
| ~ c_lessequals(X1,X2,X0)
| ~ c_lessequals(X3,X4,X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X4,X0)
| ~ class_Ring__and__Field_Opordered__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__mono_0) ).
fof(f3,axiom,
! [X2,X0,X1] :
( c_lessequals(c_0,c_times(X2,X1,X0),X0)
| ~ c_lessequals(c_0,X1,X0)
| ~ c_lessequals(c_0,X2,X0)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__nonneg__nonneg_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( ~ c_less(X1,X2,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f5,axiom,
! [X0,X1] :
( c_lessequals(c_0,c_HOL_Oabs(X1,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f6,negated_conjecture,
c_less(c_0,v_c,t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f7,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) ).
fof(f8,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) ).
fof(f9,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) ).
fof(f10,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) ).
fof(f11,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f12,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f13,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| class_Ring__and__Field_Opordered__cancel__semiring(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f14,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(f15,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(f16,plain,
class_Ring__and__Field_Opordered__cancel__semiring(t_b),
inference(resolution,[],[f13,f11]) ).
fof(f17,plain,
class_Ring__and__Field_Opordered__semiring(t_b),
inference(resolution,[],[f14,f11]) ).
fof(f18,plain,
class_OrderedGroup_Olordered__ab__group__abs(t_b),
inference(resolution,[],[f15,f11]) ).
fof(f19,plain,
class_Orderings_Oorder(t_b),
inference(resolution,[],[f18,f12]) ).
fof(f20,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(c_0,v_c,t_b) ),
inference(resolution,[],[f4,f6]) ).
fof(f21,plain,
c_lessequals(c_0,v_c,t_b),
inference(forward_subsumption_resolution,[],[f20,f19]) ).
fof(f22,plain,
! [X0,X1] : c_HOL_Oabs(c_times(X0,X1,t_b),t_b) = c_times(c_HOL_Oabs(X0,t_b),c_HOL_Oabs(X1,t_b),t_b),
inference(resolution,[],[f1,f11]) ).
fof(f28,definition,
( spl0_1
<=> c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f29,plain,
( c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f40,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| ~ c_lessequals(c_0,v_c,t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_1 ),
inference(resolution,[],[f30,f3]) ).
fof(f41,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f40,f21]) ).
fof(f42,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_f(v_x),t_b),t_b)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f41,f16]) ).
fof(f45,plain,
! [X0,X1] :
( c_lessequals(c_times(X0,X1,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(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ c_lessequals(c_0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) ),
inference(superposition,[],[f2,f9]) ).
fof(f54,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_1 ),
inference(resolution,[],[f42,f5]) ).
fof(f55,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f54,f18]) ).
fof(f56,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f57,plain,
( ! [X0,X1] :
( c_lessequals(c_times(X0,X1,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(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b)
| ~ class_Ring__and__Field_Opordered__semiring(t_b) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f45,f29]) ).
fof(f58,plain,
( ! [X0,X1] :
( c_lessequals(c_times(X0,X1,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(X1,c_times(v_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(X0,c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,X1,t_b) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f57,f17]) ).
fof(f71,plain,
( ! [X0,X1] :
( c_lessequals(c_HOL_Oabs(c_times(X0,X1,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_ca,c_HOL_Oabs(v_g(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_HOL_Oabs(X0,t_b),c_times(v_c,c_HOL_Oabs(v_f(v_x),t_b),t_b),t_b)
| ~ c_lessequals(c_0,c_HOL_Oabs(X1,t_b),t_b) )
| ~ spl0_1 ),
inference(superposition,[],[f58,f22]) ).
fof(f115,definition,
( spl0_13
<=> c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
fof(f117,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| spl0_13 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f128,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)
| ~ 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)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ spl0_1 ),
inference(resolution,[],[f71,f10]) ).
fof(f131,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)
| ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f128,f8]) ).
fof(f132,plain,
( ~ c_lessequals(c_0,c_HOL_Oabs(v_b(v_x),t_b),t_b)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f131,f7]) ).
fof(f133,plain,
( ~ spl0_13
| ~ spl0_1 ),
inference(avatar_split_clause,[],[f132,f28,f115]) ).
fof(f134,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_13 ),
inference(resolution,[],[f117,f5]) ).
fof(f135,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[],[f134,f18]) ).
fof(f136,plain,
spl0_13,
inference(avatar_contradiction_clause,[],[f135]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f56]) ).
cnf(s9,plain,
( ~ spl0_1
| ~ spl0_13 ),
inference(sat_conversion,[],[f133]) ).
cnf(s10,plain,
spl0_13,
inference(sat_conversion,[],[f136]) ).
cnf(s11,plain,
~ spl0_1,
inference(rat,[],[s9,s10]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s3,s11]) ).
fof(f137,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n014.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:32:45 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/1.16 % (2134328)Input is clausal, will run a generic CNF schedule.
% 0.21/1.16 % (2134408)lrs+10_1_sil=8000:sp=occurrence:random_seed=3256838423:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.21/1.16 % (2134408)First to succeed.
% 0.21/1.16 % (2134408)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2134328"
% 0.21/1.16 % (2134407)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2073773090:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.21/1.16 % (2134404)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2307749948:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.21/1.16 % (2134406)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3159903687:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.21/1.16 % (2134410)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=357745124:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.21/1.16 % (2134411)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1803459722:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.21/1.16 % (2134413)dis-21_1_sil=8000:lcm=predicate:random_seed=2594080163:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.21/1.16 % (2134413)Refutation not found, incomplete strategy
% 0.21/1.16 % (2134413)------------------------------
% 0.21/1.16 % (2134413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.16 % (2134413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.16 % (2134413)CaDiCaL version: 2.1.3
% 0.21/1.16 % (2134413)Termination reason: Refutation not found, incomplete strategy
% 0.21/1.16 % (2134413)Time elapsed: 0.002 s
% 0.21/1.16 % (2134413)Peak memory usage: 88 MB
% 0.21/1.16 % (2134413)Instructions burned: 1 (million)
% 0.21/1.16 % (2134411)Also succeeded, but the first one will report.
% 0.21/1.16 % (2134410)Instruction limit reached!
% 0.21/1.16 % (2134410)------------------------------
% 0.21/1.16 % (2134410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.16 % (2134410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.16 % (2134410)CaDiCaL version: 2.1.3
% 0.21/1.16 % (2134410)Termination reason: Instruction limit
% 0.21/1.16 % (2134410)Termination phase: Saturation
% 0.21/1.16 % (2134410)Time elapsed: 0.066 s
% 0.21/1.16 % (2134410)Peak memory usage: 88 MB
% 0.21/1.16 % (2134410)Instructions burned: 116 (million)
% 0.21/1.16 % (2134408)Refutation found. Thanks to Tanya!
% 0.21/1.16 % SZS status Unsatisfiable for theBenchmark
% 0.21/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/1.16 % (2134408)------------------------------
% 0.21/1.16 % (2134408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.21/1.16 % (2134408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/1.16 % (2134408)CaDiCaL version: 2.1.3
% 0.21/1.16 % (2134408)Termination reason: Refutation
% 0.21/1.16 % (2134408)Time elapsed: 0.003 s
% 0.21/1.16 % (2134408)Peak memory usage: 89 MB
% 0.21/1.16 % (2134408)Instructions burned: 6 (million)
% 0.21/1.16 % (2134408)------------------------------
% 0.21/1.16 % (2134408)------------------------------
% 0.21/1.16 % (2134328)Success in time 0.277 s
% 0.21/1.16 % Vampire exiting
%------------------------------------------------------------------------------