%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG398-1 : 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 : n018.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 0.24s 1.41s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 23 ( 14 unt; 0 def)
% Number of atoms : 39 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f696,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pc0_0) ).
fof(f717,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ofield(X0)
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| X1 = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X2,X0)
| X2 = c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).
fof(f718,plain,
! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(X1,X2,X0),X2,X0) = X1
| ~ class_Ring__and__Field_Odivision__by__zero(X0)
| ~ class_Ring__and__Field_Ofield(X0)
| c_HOL_Ozero__class_Ozero(X0) = X2 ),
inference(reorient_equations,[],[f717]) ).
fof(f944,axiom,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pqc0_0) ).
fof(f977,axiom,
! [X0,X1] : c_HOL_Oinverse__class_Odivide(X0,X1,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Oinverse__class_Oinverse(X1,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).
fof(f1056,axiom,
! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(X1,X2,X0) = c_HOL_Otimes__class_Otimes(X2,X1,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).
fof(f1057,axiom,
! [X2,X3,X0,X1] :
( c_Polynomial_Opoly(c_Polynomial_Osmult(X1,X2,X0),X3,X0) = c_HOL_Otimes__class_Otimes(X1,c_Polynomial_Opoly(X2,X3,X0),X0)
| ~ class_Ring__and__Field_Ocomm__semiring__0(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__smult_0) ).
fof(f1061,negated_conjecture,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1104,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).
fof(f1105,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).
fof(f1106,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).
fof(f1126,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).
fof(f1186,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1061,f944]) ).
fof(f1187,plain,
( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
inference(superposition,[],[f1186,f1057]) ).
fof(f1196,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[],[f1187,f1106]) ).
fof(f1202,plain,
( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
inference(superposition,[],[f1196,f1056]) ).
fof(f1221,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[],[f1202,f1105]) ).
fof(f1225,plain,
c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1221,f977]) ).
fof(f1230,plain,
( c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex) != c_Polynomial_Opoly(v_q____,v_x,tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(superposition,[],[f1225,f718]) ).
fof(f1236,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(trivial_inequality_removal,[],[f1230]) ).
fof(f1243,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(forward_subsumption_resolution,[],[f1236,f1104]) ).
fof(f1246,plain,
c_Polynomial_Opoly(v_pa____,v_c____,tc_Complex_Ocomplex) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(forward_subsumption_resolution,[],[f1243,f1126]) ).
fof(f1248,plain,
$false,
inference(forward_subsumption_resolution,[],[f1246,f696]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ALG398-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n018.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 20:19:58 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running first-order theorem proving
% 0.09/0.26 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
% 0.24/1.41 % (3726399)Input is clausal, will run a generic CNF schedule.
% 0.24/1.41 % (3726408)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1215212060:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.24/1.41 % (3726410)dis-21_1_sil=8000:lcm=predicate:random_seed=3132089934: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)
% 0.24/1.41 % (3726406)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=845328818:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.24/1.41 % (3726405)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2780016508:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.24/1.41 % (3726407)lrs+10_1_sil=8000:sp=occurrence:random_seed=2520374270:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.24/1.41 % (3726404)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=1867409442:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.24/1.41 % (3726409)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=513285987:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.24/1.41 % (3726408)Instruction limit reached!
% 0.24/1.41 % (3726408)------------------------------
% 0.24/1.41 % (3726408)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.41 % (3726408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.41 % (3726408)CaDiCaL version: 2.1.3
% 0.24/1.41 % (3726408)Termination reason: Instruction limit
% 0.24/1.41 % (3726408)Termination phase: Saturation
% 0.24/1.41 % (3726408)Time elapsed: 0.039 s
% 0.24/1.41 % (3726408)Peak memory usage: 89 MB
% 0.24/1.41 % (3726408)Instructions burned: 114 (million)
% 0.24/1.41 % (3726410)Instruction limit reached!
% 0.24/1.41 % (3726410)------------------------------
% 0.24/1.41 % (3726410)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.41 % (3726410)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.41 % (3726410)CaDiCaL version: 2.1.3
% 0.24/1.41 % (3726410)Termination reason: Instruction limit
% 0.24/1.41 % (3726410)Termination phase: Saturation
% 0.24/1.41 % (3726410)Time elapsed: 0.068 s
% 0.24/1.41 % (3726410)Peak memory usage: 90 MB
% 0.24/1.41 % (3726410)Instructions burned: 119 (million)
% 0.24/1.41 % (3726407)Instruction limit reached!
% 0.24/1.41 % (3726407)------------------------------
% 0.24/1.41 % (3726407)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.41 % (3726407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.41 % (3726407)CaDiCaL version: 2.1.3
% 0.24/1.41 % (3726407)Termination reason: Instruction limit
% 0.24/1.41 % (3726407)Termination phase: Saturation
% 0.24/1.41 % (3726407)Time elapsed: 0.075 s
% 0.24/1.41 % (3726407)Peak memory usage: 90 MB
% 0.24/1.41 % (3726407)Instructions burned: 107 (million)
% 0.24/1.41 % (3726409)Instruction limit reached!
% 0.24/1.41 % (3726409)------------------------------
% 0.24/1.41 % (3726409)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.41 % (3726409)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.41 % (3726409)CaDiCaL version: 2.1.3
% 0.24/1.41 % (3726409)Termination reason: Instruction limit
% 0.24/1.41 % (3726409)Termination phase: Saturation
% 0.24/1.41 % (3726409)Time elapsed: 0.127 s
% 0.24/1.41 % (3726409)Peak memory usage: 90 MB
% 0.24/1.41 % (3726409)Instructions burned: 181 (million)
% 0.24/1.41 % (3726418)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=2928089084:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 0.24/1.41 % (3726418)First to succeed.
% 0.24/1.41 % (3726418)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3726399"
% 0.24/1.41 % (3726420)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1839643309:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 0.24/1.41 % (3726419)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2981639268: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)
% 0.24/1.41 % (3726420)Also succeeded, but the first one will report.
% 0.24/1.41 % (3726419)Also succeeded, but the first one will report.
% 0.24/1.41 % (3726421)lrs+10_64_to=lpo:sil=8000:random_seed=545229767:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 0.24/1.41 % (3726418)Refutation found. Thanks to Tanya!
% 0.24/1.41 % SZS status Unsatisfiable for theBenchmark
% 0.24/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/1.41 % (3726418)------------------------------
% 0.24/1.41 % (3726418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.24/1.41 % (3726418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/1.41 % (3726418)CaDiCaL version: 2.1.3
% 0.24/1.41 % (3726418)Termination reason: Refutation
% 0.24/1.41 % (3726418)Time elapsed: 0.006 s
% 0.24/1.41 % (3726418)Peak memory usage: 89 MB
% 0.24/1.41 % (3726418)Instructions burned: 14 (million)
% 0.24/1.41 % (3726418)------------------------------
% 0.24/1.41 % (3726418)------------------------------
% 0.24/1.41 % (3726399)Success in time 0.509 s
% 0.24/1.41 % Vampire exiting
%------------------------------------------------------------------------------