%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ANA021-2 : 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 : n012.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 09:30:54 AM UTC 2026
% Result : Unsatisfiable 3.43s 1.13s
% Output : Refutation 3.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 6 unt; 0 def)
% Number of atoms : 18 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 11 ( 5 ~; 6 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 7 ( 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| X0 = c_Suc(c_minus(X0,c_1,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__pred_H_0) ).
fof(f2,plain,
! [X0] :
( ~ c_less(c_0,X0,tc_nat)
| c_Suc(c_minus(X0,c_1,tc_nat)) = X0 ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X0] :
( c_less(c_0,X0,tc_nat)
| X0 = c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f4,plain,
! [X0] :
( c_less(c_0,X0,tc_nat)
| c_0 = X0 ),
inference(reorient_equations,[],[f3]) ).
fof(f5,negated_conjecture,
! [X0] : c_lessequals(c_HOL_Oabs(v_f(c_Suc(X0)),t_a),c_times(v_c,c_HOL_Oabs(v_h(c_Suc(X0)),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f6,negated_conjecture,
v_x != c_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f7,plain,
c_0 != v_x,
inference(reorient_equations,[],[f6]) ).
fof(f8,negated_conjecture,
~ c_lessequals(c_HOL_Oabs(v_f(v_x),t_a),c_times(v_c,c_HOL_Oabs(v_h(v_x),t_a),t_a),t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f9,plain,
! [X0] :
( c_Suc(c_minus(X0,c_1,tc_nat)) = X0
| c_0 = X0 ),
inference(resolution,[],[f2,f4]) ).
fof(f10,plain,
! [X0] :
( c_lessequals(c_HOL_Oabs(v_f(X0),t_a),c_times(v_c,c_HOL_Oabs(v_h(X0),t_a),t_a),t_a)
| c_0 = X0 ),
inference(superposition,[],[f5,f9]) ).
fof(f11,plain,
c_0 = v_x,
inference(resolution,[],[f10,f8]) ).
fof(f12,plain,
$false,
inference(forward_subsumption_resolution,[],[f11,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA021-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.15 % Computer : n012.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Mon Sep 28 20:29:04 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 Running first-order theorem proving
% 0.09/0.18 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
% 3.43/1.13 % (3706374)Input is clausal, will run a generic CNF schedule.
% 3.43/1.13 % (3706381)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=2899719399:i=140167_3000 on theBenchmark for (3000ds/140167Mi)
% 3.43/1.13 % (3706384)lrs+10_1_sil=8000:sp=occurrence:random_seed=3948220736:i=107:sd=3:ss=axioms:sgt=8_3000 on theBenchmark for (3000ds/107Mi)
% 3.43/1.13 % (3706383)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1188544474:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_3000 on theBenchmark for (3000ds/137899Mi)
% 3.43/1.13 % (3706385)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=4178784474:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_3000 on theBenchmark for (3000ds/114Mi)
% 3.43/1.13 % (3706382)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4275547166:i=132376:av=off_3000 on theBenchmark for (3000ds/132376Mi)
% 3.43/1.13 % (3706385)Refutation not found, incomplete strategy
% 3.43/1.13 % (3706385)------------------------------
% 3.43/1.13 % (3706385)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.13 % (3706385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.13 % (3706385)CaDiCaL version: 2.1.3
% 3.43/1.13 % (3706385)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.13 % (3706385)Time elapsed: 0.001 s
% 3.43/1.13 % (3706385)Peak memory usage: 87 MB
% 3.43/1.13 % (3706384)First to succeed.
% 3.43/1.13 % (3706384)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3706374"
% 3.43/1.13 % (3706387)dis-21_1_sil=8000:lcm=predicate:random_seed=2636938369:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/117Mi)
% 3.43/1.13 % (3706386)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2320015647:s2a=on:i=180:gtg=position_3000 on theBenchmark for (3000ds/180Mi)
% 3.43/1.13 % (3706387)Refutation not found, incomplete strategy
% 3.43/1.13 % (3706387)------------------------------
% 3.43/1.13 % (3706387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.13 % (3706387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.13 % (3706387)CaDiCaL version: 2.1.3
% 3.43/1.13 % (3706387)Termination reason: Refutation not found, incomplete strategy
% 3.43/1.13 % (3706387)Time elapsed: 0.001 s
% 3.43/1.13 % (3706387)Peak memory usage: 88 MB
% 3.43/1.13 % (3706386)Also succeeded, but the first one will report.
% 3.43/1.13 % (3706385)------------------------------
% 3.43/1.13 % (3706385)------------------------------
% 3.43/1.13 % (3706384)Refutation found. Thanks to Tanya!
% 3.43/1.13 % SZS status Unsatisfiable for theBenchmark
% 3.43/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 3.43/1.13 % (3706384)------------------------------
% 3.43/1.13 % (3706384)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.43/1.13 % (3706384)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.43/1.13 % (3706384)CaDiCaL version: 2.1.3
% 3.43/1.13 % (3706384)Termination reason: Refutation
% 3.43/1.13 % (3706384)Time elapsed: 0.001 s
% 3.43/1.13 % (3706384)Peak memory usage: 88 MB
% 3.43/1.13 % (3706384)Instructions burned: 1 (million)
% 3.43/1.13 % (3706384)------------------------------
% 3.43/1.13 % (3706384)------------------------------
% 3.43/1.13 % (3706374)Success in time 0.43 s
% 3.43/1.13 % Vampire exiting
%------------------------------------------------------------------------------