%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG376-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 09:19:53 AM UTC 2026
% Result : Unsatisfiable 0.20s 1.41s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 26 ( 14 unt; 2 def)
% Number of atoms : 38 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 25 ( 13 ~; 10 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-3 aty)
% Number of functors : 22 ( 22 usr; 10 con; 0-3 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f911,axiom,
! [X0,X1] : c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__diff__def_0) ).
fof(f912,plain,
! [X0,X1] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),
inference(reorient_equations,[],[f911]) ).
fof(f914,axiom,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X1,c_HOL_Ouminus__class_Ouminus(X0,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__add__cancel_0) ).
fof(f1008,axiom,
! [X0,X1] : c_lessequals(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add1_0) ).
fof(f1155,axiom,
! [X0] :
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X0,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_th1_0) ).
fof(f1304,axiom,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal)
| ~ c_lessequals(v_N1____,c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f1305,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1483,definition,
( spl0_1
<=> c_lessequals(v_N1____,c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat),tc_nat) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f1485,plain,
( ~ c_lessequals(v_N1____,c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat),tc_nat)
| spl0_1 ),
inference(avatar_component_clause,[],[f1483]) ).
fof(f1487,definition,
( spl0_2
<=> c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f1489,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f1487]) ).
fof(f1490,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f1304,f1487,f1483]) ).
fof(f1493,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f1485,f1008]) ).
fof(f1494,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f1493]) ).
fof(f2001,plain,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ouminus__class_Ouminus(X1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f914,f912]) ).
fof(f2002,plain,
! [X0,X1] : c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X1,X0,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(X0,X1,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(forward_demodulation,[],[f2001,f912]) ).
fof(f2007,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(superposition,[],[f1305,f2002]) ).
fof(f3056,plain,
! [X0] :
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(X0,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_d____,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,X0,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(forward_demodulation,[],[f1155,f2002]) ).
fof(f3073,plain,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(v_p,v_g____(v_f____(c_HOL_Oplus__class_Oplus(v_N1____,v_N2____,tc_nat))),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v_s____,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_p,v_z____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ spl0_2 ),
inference(resolution,[],[f3056,f1489]) ).
fof(f3076,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f3073,f2007]) ).
fof(f3077,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f3076]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f1490]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f1494]) ).
cnf(s75,plain,
~ spl0_2,
inference(sat_conversion,[],[f3077]) ).
cnf(s81,plain,
$false,
inference(rat,[],[s1,s75,s2]) ).
fof(f3078,plain,
$false,
inference(avatar_sat_refutation,[],[s81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG376-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n015.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Mon Sep 28 20:17:32 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running first-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.34/1.21 % (2963489)Input is clausal, will run a generic CNF schedule.
% 3.34/1.21 % (2963498)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3328118656:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.34/1.21 % (2963494)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=4033012114:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.34/1.21 % (2963498)Instruction limit reached!
% 3.34/1.21 % (2963498)------------------------------
% 3.34/1.21 % (2963498)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.21 % (2963498)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.21 % (2963498)CaDiCaL version: 2.1.3
% 3.34/1.21 % (2963498)Termination reason: Instruction limit
% 3.34/1.21 % (2963498)Termination phase: Saturation
% 3.34/1.21 % (2963498)Time elapsed: 0.042 s
% 3.34/1.21 % (2963498)Peak memory usage: 90 MB
% 3.34/1.21 % (2963498)Instructions burned: 117 (million)
% 3.34/1.21 % (2963499)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=38332024:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.34/1.21 % (2963496)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3303222328:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.34/1.21 % (2963495)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3021733814:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.34/1.21 % (2963497)lrs+10_1_sil=8000:sp=occurrence:random_seed=3320813416:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.34/1.21 % (2963500)dis-21_1_sil=8000:lcm=predicate:random_seed=2192977089: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)
% 3.34/1.21 % (2963500)Instruction limit reached!
% 3.34/1.21 % (2963500)------------------------------
% 3.34/1.21 % (2963500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.21 % (2963500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.21 % (2963500)CaDiCaL version: 2.1.3
% 3.34/1.21 % (2963500)Termination reason: Instruction limit
% 3.34/1.21 % (2963500)Termination phase: Saturation
% 3.34/1.21 % (2963500)Time elapsed: 0.059 s
% 3.34/1.21 % (2963500)Peak memory usage: 89 MB
% 3.34/1.21 % (2963500)Instructions burned: 119 (million)
% 3.34/1.21 % (2963497)Instruction limit reached!
% 3.34/1.21 % (2963497)------------------------------
% 3.34/1.21 % (2963497)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.21 % (2963497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.21 % (2963497)CaDiCaL version: 2.1.3
% 3.34/1.21 % (2963497)Termination reason: Instruction limit
% 3.34/1.21 % (2963497)Termination phase: Saturation
% 3.34/1.21 % (2963497)Time elapsed: 0.070 s
% 3.34/1.21 % (2963497)Peak memory usage: 90 MB
% 3.34/1.21 % (2963497)Instructions burned: 108 (million)
% 3.34/1.21 % (2963506)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=3447000842:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 3.34/1.21 % (2963499)First to succeed.
% 3.34/1.21 % (2963499)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2963489"
% 3.34/1.21 % (2963506)Also succeeded, but the first one will report.
% 3.34/1.21 % (2963509)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=4015371003: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)
% 3.34/1.21 % (2963510)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=853927472:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 3.34/1.21 % (2963509)Instruction limit reached!
% 3.34/1.21 % (2963509)------------------------------
% 3.34/1.21 % (2963509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.21 % (2963509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.21 % (2963509)CaDiCaL version: 2.1.3
% 3.34/1.21 % (2963509)Termination reason: Instruction limit
% 3.34/1.21 % (2963509)Termination phase: Saturation
% 3.34/1.21 % (2963509)Time elapsed: 0.100 s
% 3.34/1.21 % (2963509)Peak memory usage: 91 MB
% 3.34/1.21 % (2963509)Instructions burned: 191 (million)
% 0.20/1.41 % (2963514)lrs+10_64_to=lpo:sil=8000:random_seed=1698709913:i=126:bd=preordered_2995 on theBenchmark for (2995ds/126Mi)
% 0.20/1.41 % (2963510)Instruction limit reached!
% 0.20/1.41 % (2963510)------------------------------
% 0.20/1.41 % (2963510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.41 % (2963510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.41 % (2963510)CaDiCaL version: 2.1.3
% 0.20/1.41 % (2963510)Termination reason: Instruction limit
% 0.20/1.41 % (2963510)Termination phase: Saturation
% 0.20/1.41 % (2963510)Time elapsed: 0.121 s
% 0.20/1.41 % (2963510)Peak memory usage: 91 MB
% 0.20/1.41 % (2963510)Instructions burned: 219 (million)
% 0.20/1.41 % (2963499)Refutation found. Thanks to Tanya!
% 0.20/1.41 % SZS status Unsatisfiable for theBenchmark
% 0.20/1.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/1.41 % (2963499)------------------------------
% 0.20/1.41 % (2963499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.20/1.41 % (2963499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/1.41 % (2963499)CaDiCaL version: 2.1.3
% 0.20/1.41 % (2963499)Termination reason: Refutation
% 0.20/1.41 % (2963499)Time elapsed: 0.094 s
% 0.20/1.41 % (2963499)Peak memory usage: 91 MB
% 0.20/1.41 % (2963499)Instructions burned: 150 (million)
% 0.20/1.41 % (2963499)------------------------------
% 0.20/1.41 % (2963499)------------------------------
% 0.20/1.41 % (2963489)Success in time 0.544 s
% 0.20/1.41 % Vampire exiting
%------------------------------------------------------------------------------