%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG402-1 : 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 : n004.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 09:19:56 AM UTC 2026
% Result : Unsatisfiable 4.30s 1.42s
% Output : Refutation 4.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 21 ( 14 unt; 0 def)
% Number of atoms : 28 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 17 ( 10 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f85,axiom,
! [X0] :
( c_HOL_Ozero__class_Ozero(X0) != c_HOL_Oone__class_Oone(X0)
| ~ class_Ring__and__Field_Ozero__neq__one(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f355,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).
fof(f535,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) = c_HOL_Oone__class_Oone(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).
fof(f536,plain,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_HOL_Oone__class_Oone(X0) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(X0),X1,X0) ),
inference(reorient_equations,[],[f535]) ).
fof(f851,axiom,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).
fof(f1030,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).
fof(f1031,plain,
! [X0,X1] :
( ~ class_Ring__and__Field_Oring__no__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
inference(reorient_equations,[],[f1030]) ).
fof(f1139,negated_conjecture,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1222,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).
fof(f1236,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).
fof(f1242,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).
fof(f1260,plain,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X1,c_Power_Opower__class_Opower(X1,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[],[f1139,f851]) ).
fof(f3206,plain,
! [X0] : c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex) = X0,
inference(resolution,[],[f355,f1242]) ).
fof(f3661,plain,
! [X0] : c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) = c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(resolution,[],[f536,f1242]) ).
fof(f3700,plain,
! [X0] : c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),X0,tc_Complex_Ocomplex),
inference(resolution,[],[f1031,f1222]) ).
fof(f4486,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(superposition,[],[f1260,f3661]) ).
fof(f4487,plain,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Power_Opower__class_Opower(X0,c_HOL_Ominus__class_Ominus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f4486,f3206]) ).
fof(f4822,plain,
c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
inference(superposition,[],[f3700,f4487]) ).
fof(f4854,plain,
( c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ),
inference(superposition,[],[f85,f4822]) ).
fof(f4855,plain,
~ class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
inference(trivial_inequality_removal,[],[f4854]) ).
fof(f4856,plain,
$false,
inference(forward_subsumption_resolution,[],[f4855,f1236]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG402-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n004.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Mon Sep 28 20:18:37 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.24 Running first-order theorem proving
% 0.08/0.24 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
% 4.30/1.42 % (714791)Input is clausal, will run a generic CNF schedule.
% 4.30/1.42 % (714800)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2794784277:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.30/1.42 % (714801)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3865647225:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.30/1.42 % (714797)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3831493373:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.30/1.42 % (714799)lrs+10_1_sil=8000:sp=occurrence:random_seed=2628315815:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.30/1.42 % (714796)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=2865159228:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.30/1.42 % (714798)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=4216903983:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.30/1.42 % (714802)dis-21_1_sil=8000:lcm=predicate:random_seed=2979303736: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)
% 4.30/1.42 % (714800)Instruction limit reached!
% 4.30/1.42 % (714800)------------------------------
% 4.30/1.42 % (714800)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.42 % (714800)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.42 % (714800)CaDiCaL version: 2.1.3
% 4.30/1.42 % (714800)Termination reason: Instruction limit
% 4.30/1.42 % (714800)Termination phase: Saturation
% 4.30/1.42 % (714800)Time elapsed: 0.040 s
% 4.30/1.42 % (714800)Peak memory usage: 89 MB
% 4.30/1.42 % (714800)Instructions burned: 116 (million)
% 4.30/1.42 % (714802)Instruction limit reached!
% 4.30/1.42 % (714802)------------------------------
% 4.30/1.42 % (714802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.42 % (714802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.42 % (714802)CaDiCaL version: 2.1.3
% 4.30/1.42 % (714802)Termination reason: Instruction limit
% 4.30/1.42 % (714802)Termination phase: Saturation
% 4.30/1.42 % (714802)Time elapsed: 0.067 s
% 4.30/1.42 % (714802)Peak memory usage: 89 MB
% 4.30/1.42 % (714802)Instructions burned: 117 (million)
% 4.30/1.42 % (714799)Instruction limit reached!
% 4.30/1.42 % (714799)------------------------------
% 4.30/1.42 % (714799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.42 % (714799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.42 % (714799)CaDiCaL version: 2.1.3
% 4.30/1.42 % (714799)Termination reason: Instruction limit
% 4.30/1.42 % (714799)Termination phase: Saturation
% 4.30/1.42 % (714799)Time elapsed: 0.069 s
% 4.30/1.42 % (714799)Peak memory usage: 89 MB
% 4.30/1.42 % (714799)Instructions burned: 107 (million)
% 4.30/1.42 % (714810)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=3346256905:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 4.30/1.42 % (714801)First to succeed.
% 4.30/1.42 % (714801)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-714791"
% 4.30/1.42 % (714810)Instruction limit reached!
% 4.30/1.42 % (714810)------------------------------
% 4.30/1.42 % (714810)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.42 % (714810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.42 % (714810)CaDiCaL version: 2.1.3
% 4.30/1.42 % (714810)Termination reason: Instruction limit
% 4.30/1.42 % (714810)Termination phase: Saturation
% 4.30/1.42 % (714810)Time elapsed: 0.042 s
% 4.30/1.42 % (714810)Peak memory usage: 90 MB
% 4.30/1.42 % (714810)Instructions burned: 146 (million)
% 4.30/1.42 % (714812)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=3303193887:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 4.30/1.42 % (714811)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=1087036093: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)
% 4.30/1.42 % (714814)lrs+10_64_to=lpo:sil=8000:random_seed=1876994512:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 4.30/1.42 % (714812)Also succeeded, but the first one will report.
% 4.30/1.42 % (714814)Also succeeded, but the first one will report.
% 4.30/1.42 % (714811)Instruction limit reached!
% 4.30/1.42 % (714811)------------------------------
% 4.30/1.42 % (714811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.42 % (714811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.42 % (714811)CaDiCaL version: 2.1.3
% 4.30/1.42 % (714811)Termination reason: Instruction limit
% 4.30/1.42 % (714811)Termination phase: Saturation
% 4.30/1.42 % (714811)Time elapsed: 0.103 s
% 4.30/1.42 % (714811)Peak memory usage: 91 MB
% 4.30/1.42 % (714811)Instructions burned: 189 (million)
% 4.30/1.42 % (714801)Refutation found. Thanks to Tanya!
% 4.30/1.42 % SZS status Unsatisfiable for theBenchmark
% 4.30/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 4.30/1.42 % (714801)------------------------------
% 4.30/1.42 % (714801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.30/1.42 % (714801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.30/1.42 % (714801)CaDiCaL version: 2.1.3
% 4.30/1.42 % (714801)Termination reason: Refutation
% 4.30/1.42 % (714801)Time elapsed: 0.106 s
% 4.30/1.42 % (714801)Peak memory usage: 90 MB
% 4.30/1.42 % (714801)Instructions burned: 165 (million)
% 4.30/1.42 % (714801)------------------------------
% 4.30/1.42 % (714801)------------------------------
% 4.30/1.42 % (714791)Success in time 0.549 s
% 4.30/1.42 % Vampire exiting
%------------------------------------------------------------------------------