%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG363-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:19:52 AM UTC 2026
% Result : Unsatisfiable 2.75s 1.15s
% Output : Refutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 40 ( 18 unt; 1 def)
% Number of atoms : 63 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 23 ~; 22 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-3 aty)
% Number of variables : 21 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f584,axiom,
! [X0] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__gt__zero_0) ).
fof(f590,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).
fof(f600,axiom,
! [X0] : ~ c_HOL_Oord__class_Oless(X0,X0,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).
fof(f607,axiom,
! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_RealDef_Oreal)
| c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).
fof(f613,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__abs__def_1) ).
fof(f675,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rp_0) ).
fof(f676,axiom,
! [X0] : c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(X0)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_th_0) ).
fof(f698,axiom,
! [X0,X1] :
( ~ c_lessequals(X1,X0,tc_RealDef_Oreal)
| X0 = X1
| ~ c_lessequals(X0,X1,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).
fof(f759,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f761,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f767,negated_conjecture,
( ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(v_s(v_f____(v_x))),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f792,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).
fof(f854,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_subsumption_resolution,[],[f767,f676]) ).
fof(f870,plain,
! [X0] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),X0,tc_RealDef_Oreal) = X0,
inference(resolution,[],[f759,f792]) ).
fof(f874,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = X0,
inference(resolution,[],[f761,f792]) ).
fof(f886,plain,
c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(resolution,[],[f613,f600]) ).
fof(f887,plain,
! [X0] :
( c_lessequals(X0,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oabs__class_Oabs(X0,tc_RealDef_Oreal) = X0 ),
inference(resolution,[],[f613,f607]) ).
fof(f902,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[],[f584,f886]) ).
fof(f903,plain,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f902,f874]) ).
fof(f905,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X1,X0,tc_RealDef_Oreal),
inference(resolution,[],[f590,f792]) ).
fof(f922,definition,
( spl0_2
<=> c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f923,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != v_r
| spl0_2 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f924,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f922]) ).
fof(f930,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_2 ),
inference(superposition,[],[f854,f924]) ).
fof(f932,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(v_r,X0,tc_RealDef_Oreal) = X0
| ~ spl0_2 ),
inference(superposition,[],[f870,f924]) ).
fof(f938,plain,
( c_HOL_Oord__class_Oless(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_2 ),
inference(superposition,[],[f903,f924]) ).
fof(f940,plain,
( ~ c_HOL_Oord__class_Oless(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_2 ),
inference(forward_demodulation,[],[f930,f932]) ).
fof(f942,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f940,f938]) ).
fof(f943,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f942]) ).
fof(f948,plain,
( c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) = v_r
| ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(resolution,[],[f698,f675]) ).
fof(f955,plain,
( ~ c_lessequals(v_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f948,f923]) ).
fof(f1607,plain,
( v_r = c_HOL_Oabs__class_Oabs(v_r,tc_RealDef_Oreal)
| spl0_2 ),
inference(resolution,[],[f887,f955]) ).
fof(f1620,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_2 ),
inference(superposition,[],[f584,f1607]) ).
fof(f1629,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| spl0_2 ),
inference(forward_demodulation,[],[f1620,f905]) ).
fof(f1630,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f1629,f854]) ).
fof(f1631,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f1630]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f943]) ).
cnf(s20,plain,
spl0_2,
inference(sat_conversion,[],[f1631]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s2,s20]) ).
fof(f1632,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG363-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:19:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 2.75/1.15 % (678966)Input is clausal, will run a generic CNF schedule.
% 2.75/1.15 % (678974)lrs+10_1_sil=8000:sp=occurrence:random_seed=3696027552:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.75/1.15 % (678974)First to succeed.
% 2.75/1.15 % (678974)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-678966"
% 2.75/1.15 % (678976)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1772085651:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.75/1.15 % (678972)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2969136934:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.75/1.15 % (678973)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2450457511:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.75/1.15 % (678971)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=218418272:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.75/1.15 % (678975)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2151322315:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.75/1.15 % (678977)dis-21_1_sil=8000:lcm=predicate:random_seed=3354734384: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)
% 2.75/1.15 % (678975)Also succeeded, but the first one will report.
% 2.75/1.15 % (678976)Also succeeded, but the first one will report.
% 2.75/1.15 % (678977)Instruction limit reached!
% 2.75/1.15 % (678977)------------------------------
% 2.75/1.15 % (678977)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.15 % (678977)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.15 % (678977)CaDiCaL version: 2.1.3
% 2.75/1.15 % (678977)Termination reason: Instruction limit
% 2.75/1.15 % (678977)Termination phase: Saturation
% 2.75/1.15 % (678977)Time elapsed: 0.068 s
% 2.75/1.15 % (678977)Peak memory usage: 90 MB
% 2.75/1.15 % (678977)Instructions burned: 119 (million)
% 2.75/1.15 % (678974)Refutation found. Thanks to Tanya!
% 2.75/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.75/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.75/1.15 % (678974)------------------------------
% 2.75/1.15 % (678974)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.75/1.15 % (678974)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.75/1.15 % (678974)CaDiCaL version: 2.1.3
% 2.75/1.15 % (678974)Termination reason: Refutation
% 2.75/1.15 % (678974)Time elapsed: 0.015 s
% 2.75/1.15 % (678974)Peak memory usage: 90 MB
% 2.75/1.15 % (678974)Instructions burned: 35 (million)
% 2.75/1.15 % (678974)------------------------------
% 2.75/1.15 % (678974)------------------------------
% 2.75/1.15 % (678966)Success in time 0.319 s
% 2.75/1.15 % Vampire exiting
%------------------------------------------------------------------------------