%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA044-1 : 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 : n013.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 09:31:00 AM UTC 2026
% Result : Unsatisfiable 5.29s 1.60s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 29 ( 10 unt; 2 def)
% Number of atoms : 55 ( 3 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 53 ( 27 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 10 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1434,axiom,
! [X0,X1] :
( c_HOL_Oabs(X1,X0) = X1
| ~ c_lessequals(c_0,X1,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f3033,axiom,
! [X0] :
( class_Ring__and__Field_Opordered__cancel__semiring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f3044,axiom,
! [X0] :
( class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f3362,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(f3365,negated_conjecture,
! [X0,X1] : c_lessequals(c_0,v_l(X0,X1),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3366,negated_conjecture,
! [X0] : c_lessequals(c_0,v_h(X0),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3368,negated_conjecture,
c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_HOL_Oabs(c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3369,negated_conjecture,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tfree_tcs) ).
fof(f3436,plain,
( c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b) != c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b)
| ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(superposition,[],[f3368,f1434]) ).
fof(f3438,plain,
( ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
inference(trivial_inequality_removal,[],[f3436]) ).
fof(f3440,definition,
( spl0_1
<=> class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f3442,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| spl0_1 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f3453,definition,
( spl0_4
<=> c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f3455,plain,
( ~ c_lessequals(c_0,c_times(v_l(v_x,v_xa),v_h(v_k(v_x,v_xa)),t_b),t_b)
| spl0_4 ),
inference(avatar_component_clause,[],[f3453]) ).
fof(f3456,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f3438,f3453,f3440]) ).
fof(f3584,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_1 ),
inference(resolution,[],[f3442,f3044]) ).
fof(f3585,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f3584,f3369]) ).
fof(f3586,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f3585]) ).
fof(f3608,plain,
( ~ c_lessequals(c_0,v_h(v_k(v_x,v_xa)),t_b)
| ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_4 ),
inference(resolution,[],[f3455,f3362]) ).
fof(f3609,plain,
( ~ c_lessequals(c_0,v_l(v_x,v_xa),t_b)
| ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f3608,f3366]) ).
fof(f3610,plain,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f3609,f3365]) ).
fof(f3611,plain,
( ~ class_Ring__and__Field_Oordered__idom(t_b)
| spl0_4 ),
inference(resolution,[],[f3610,f3033]) ).
fof(f3614,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[],[f3611,f3369]) ).
fof(f3615,plain,
spl0_4,
inference(avatar_contradiction_clause,[],[f3614]) ).
cnf(s2,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f3456]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f3586]) ).
cnf(s4,plain,
spl0_4,
inference(sat_conversion,[],[f3615]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s2,s4,s3]) ).
fof(f3616,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA044-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n013.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 20:33:22 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 5.29/1.60 % (1520818)Input is clausal, will run a generic CNF schedule.
% 5.29/1.60 % (1520824)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1932925643:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 5.29/1.60 % (1520826)lrs+10_1_sil=8000:sp=occurrence:random_seed=3279904464:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 5.29/1.60 % (1520828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=685493654:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 5.29/1.60 % (1520829)dis-21_1_sil=8000:lcm=predicate:random_seed=2424211191: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)
% 5.29/1.60 % (1520823)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=2086343129:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 5.29/1.60 % (1520825)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3553977093:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 5.29/1.60 % (1520827)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=122622347:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 5.29/1.60 % (1520829)Instruction limit reached!
% 5.29/1.60 % (1520829)------------------------------
% 5.29/1.60 % (1520829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520829)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520829)Termination reason: Instruction limit
% 5.29/1.60 % (1520829)Termination phase: Saturation
% 5.29/1.60 % (1520829)Time elapsed: 0.060 s
% 5.29/1.60 % (1520829)Peak memory usage: 90 MB
% 5.29/1.60 % (1520829)Instructions burned: 118 (million)
% 5.29/1.60 % (1520827)Instruction limit reached!
% 5.29/1.60 % (1520827)------------------------------
% 5.29/1.60 % (1520827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520827)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520827)Termination reason: Instruction limit
% 5.29/1.60 % (1520827)Termination phase: Saturation
% 5.29/1.60 % (1520827)Time elapsed: 0.069 s
% 5.29/1.60 % (1520827)Peak memory usage: 90 MB
% 5.29/1.60 % (1520827)Instructions burned: 115 (million)
% 5.29/1.60 % (1520826)Instruction limit reached!
% 5.29/1.60 % (1520826)------------------------------
% 5.29/1.60 % (1520826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520826)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520826)Termination reason: Instruction limit
% 5.29/1.60 % (1520826)Termination phase: Saturation
% 5.29/1.60 % (1520826)Time elapsed: 0.074 s
% 5.29/1.60 % (1520826)Peak memory usage: 91 MB
% 5.29/1.60 % (1520826)Instructions burned: 107 (million)
% 5.29/1.60 % (1520828)Instruction limit reached!
% 5.29/1.60 % (1520828)------------------------------
% 5.29/1.60 % (1520828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520828)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520828)Termination reason: Instruction limit
% 5.29/1.60 % (1520828)Termination phase: Saturation
% 5.29/1.60 % (1520828)Time elapsed: 0.110 s
% 5.29/1.60 % (1520828)Peak memory usage: 91 MB
% 5.29/1.60 % (1520828)Instructions burned: 181 (million)
% 5.29/1.60 % (1520837)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=740782918:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 5.29/1.60 % (1520837)Refutation not found, incomplete strategy
% 5.29/1.60 % (1520837)------------------------------
% 5.29/1.60 % (1520837)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520837)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520837)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520837)Termination reason: Refutation not found, incomplete strategy
% 5.29/1.60 % (1520837)Time elapsed: 0.012 s
% 5.29/1.60 % (1520837)Peak memory usage: 90 MB
% 5.29/1.60 % (1520837)Instructions burned: 16 (million)
% 5.29/1.60 % (1520839)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3436121690:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 5.29/1.60 % (1520838)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1394413824:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 5.29/1.60 % (1520839)First to succeed.
% 5.29/1.60 % (1520839)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1520818"
% 5.29/1.60 % (1520840)lrs+10_64_to=lpo:sil=8000:random_seed=3145435381:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 5.29/1.60 % (1520838)Instruction limit reached!
% 5.29/1.60 % (1520838)------------------------------
% 5.29/1.60 % (1520838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520838)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520838)Termination reason: Instruction limit
% 5.29/1.60 % (1520838)Termination phase: Saturation
% 5.29/1.60 % (1520838)Time elapsed: 0.103 s
% 5.29/1.60 % (1520838)Peak memory usage: 92 MB
% 5.29/1.60 % (1520838)Instructions burned: 194 (million)
% 5.29/1.60 % (1520840)Instruction limit reached!
% 5.29/1.60 % (1520840)------------------------------
% 5.29/1.60 % (1520840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520840)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520840)Termination reason: Instruction limit
% 5.29/1.60 % (1520840)Termination phase: Saturation
% 5.29/1.60 % (1520840)Time elapsed: 0.072 s
% 5.29/1.60 % (1520840)Peak memory usage: 92 MB
% 5.29/1.60 % (1520840)Instructions burned: 126 (million)
% 5.29/1.60 % (1520837)------------------------------
% 5.29/1.60 % (1520837)------------------------------
% 5.29/1.60 % (1520846)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2283901728:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 5.29/1.60 % (1520845)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=831814151:avsq=on:i=194:fgj=on:bd=preordered_2994 on theBenchmark for (2994ds/194Mi)
% 5.29/1.60 % (1520839)Refutation found. Thanks to Tanya!
% 5.29/1.60 % SZS status Unsatisfiable for theBenchmark
% 5.29/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 5.29/1.60 % (1520839)------------------------------
% 5.29/1.60 % (1520839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.60 % (1520839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.60 % (1520839)CaDiCaL version: 2.1.3
% 5.29/1.60 % (1520839)Termination reason: Refutation
% 5.29/1.60 % (1520839)Time elapsed: 0.041 s
% 5.29/1.60 % (1520839)Peak memory usage: 92 MB
% 5.29/1.60 % (1520839)Instructions burned: 66 (million)
% 5.29/1.60 % (1520839)------------------------------
% 5.29/1.60 % (1520839)------------------------------
% 5.29/1.60 % (1520818)Success in time 0.73 s
% 5.29/1.60 % Vampire exiting
%------------------------------------------------------------------------------