%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV633-1 : 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 : n017.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 01:19:08 PM UTC 2026
% Result : Unsatisfiable 4.84s 1.66s
% Output : Refutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 23 ( 23 unt; 0 def)
% Number of atoms : 23 ( 22 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 11 ( 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1411,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__1__eq__Suc__0_0) ).
fof(f1412,plain,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
inference(reorient_equations,[],[f1411]) ).
fof(f1456,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_numeral__2__eq__2_0) ).
fof(f1457,plain,
c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),
inference(reorient_equations,[],[f1456]) ).
fof(f1628,axiom,
c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat) = c_HOL_Oone__class_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__numeral__1__eq__1_0) ).
fof(f1629,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),
inference(reorient_equations,[],[f1628]) ).
fof(f1660,axiom,
! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X0,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__2__right_0) ).
fof(f1661,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat),
inference(reorient_equations,[],[f1660]) ).
fof(f1690,axiom,
! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),X2,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
fof(f1716,axiom,
! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f1723,negated_conjecture,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1858,plain,
c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),
inference(forward_demodulation,[],[f1412,f1629]) ).
fof(f1888,plain,
c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat) = c_Suc(c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f1457,f1858]) ).
fof(f1890,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(superposition,[],[f1723,f1888]) ).
fof(f1891,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1890,f1716]) ).
fof(f1892,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1891,f1716]) ).
fof(f1911,plain,
! [X0] : c_HOL_Oplus__class_Oplus(X0,X0,tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(forward_demodulation,[],[f1661,f1888]) ).
fof(f1980,plain,
! [X2,X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_HOL_Otimes__class_Otimes(X1,X2,tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X0,tc_nat),tc_nat),
inference(superposition,[],[f1690,f1716]) ).
fof(f2153,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Otimes__class_Otimes(v_m,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f1892,f1911]) ).
fof(f2154,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Otimes__class_Otimes(v_i,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f2153,f1911]) ).
fof(f5171,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Otimes__class_Otimes(v_j,c_Suc(c_HOL_Oone__class_Oone(tc_nat)),tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(superposition,[],[f2154,f1980]) ).
fof(f5222,plain,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex) != c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(c_HOL_Oplus__class_Oplus(v_m,v_m,tc_nat)),c_HOL_Otimes__class_Otimes(v_i,c_HOL_Oplus__class_Oplus(v_j,v_j,tc_nat),tc_nat),tc_Complex_Ocomplex),
inference(forward_demodulation,[],[f5171,f1911]) ).
fof(f5223,plain,
$false,
inference(trivial_inequality_removal,[],[f5222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV633-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n017.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 12:02:09 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.84/1.66 % (3499568)Input is clausal, will run a generic CNF schedule.
% 4.84/1.66 % (3499601)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=766320779:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 4.84/1.66 % (3499600)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=2105054750:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 4.84/1.66 % (3499604)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3672446324:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 4.84/1.66 % (3499602)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=119843521:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 4.84/1.66 % (3499603)lrs+10_1_sil=8000:sp=occurrence:random_seed=226459105:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 4.84/1.66 % (3499605)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1974194679:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 4.84/1.66 % (3499606)dis-21_1_sil=8000:lcm=predicate:random_seed=1140181827: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)
% 4.84/1.66 % (3499603)Instruction limit reached!
% 4.84/1.66 % (3499603)------------------------------
% 4.84/1.66 % (3499603)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.66 % (3499603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.66 % (3499603)CaDiCaL version: 2.1.3
% 4.84/1.66 % (3499603)Termination reason: Instruction limit
% 4.84/1.66 % (3499603)Termination phase: Saturation
% 4.84/1.66 % (3499603)Time elapsed: 0.072 s
% 4.84/1.66 % (3499603)Peak memory usage: 90 MB
% 4.84/1.66 % (3499603)Instructions burned: 108 (million)
% 4.84/1.66 % (3499604)Instruction limit reached!
% 4.84/1.66 % (3499604)------------------------------
% 4.84/1.66 % (3499604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.66 % (3499604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.66 % (3499604)CaDiCaL version: 2.1.3
% 4.84/1.66 % (3499604)Termination reason: Instruction limit
% 4.84/1.66 % (3499604)Termination phase: Saturation
% 4.84/1.66 % (3499604)Time elapsed: 0.074 s
% 4.84/1.66 % (3499604)Peak memory usage: 90 MB
% 4.84/1.66 % (3499604)Instructions burned: 115 (million)
% 4.84/1.66 % (3499606)Instruction limit reached!
% 4.84/1.66 % (3499606)------------------------------
% 4.84/1.66 % (3499606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.66 % (3499606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.66 % (3499606)CaDiCaL version: 2.1.3
% 4.84/1.66 % (3499606)Termination reason: Instruction limit
% 4.84/1.66 % (3499606)Termination phase: Saturation
% 4.84/1.66 % (3499606)Time elapsed: 0.065 s
% 4.84/1.66 % (3499606)Peak memory usage: 90 MB
% 4.84/1.66 % (3499606)Instructions burned: 117 (million)
% 4.84/1.66 % (3499605)First to succeed.
% 4.84/1.66 % (3499605)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3499568"
% 4.84/1.66 % (3499617)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=2256166073:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2996 on theBenchmark for (2996ds/189Mi)
% 4.84/1.66 % (3499616)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=3562849063:i=143:sd=2:aac=none:ss=axioms:sgt=16_2996 on theBenchmark for (2996ds/143Mi)
% 4.84/1.66 % (3499618)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=2554303597:st=4:i=219:sd=3:ss=axioms_2996 on theBenchmark for (2996ds/219Mi)
% 4.84/1.66 % (3499616)Also succeeded, but the first one will report.
% 4.84/1.66 % (3499618)Also succeeded, but the first one will report.
% 4.84/1.66 % (3499617)Also succeeded, but the first one will report.
% 4.84/1.66 % (3499605)Refutation found. Thanks to Tanya!
% 4.84/1.66 % SZS status Unsatisfiable for theBenchmark
% 4.84/1.66 % SZS output start Proof for theBenchmark
% See solution above
% 4.84/1.66 % (3499605)------------------------------
% 4.84/1.66 % (3499605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.84/1.66 % (3499605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.84/1.66 % (3499605)CaDiCaL version: 2.1.3
% 4.84/1.66 % (3499605)Termination reason: Refutation
% 4.84/1.66 % (3499605)Time elapsed: 0.124 s
% 4.84/1.66 % (3499605)Peak memory usage: 91 MB
% 4.84/1.66 % (3499605)Instructions burned: 183 (million)
% 4.84/1.66 % (3499605)------------------------------
% 4.84/1.66 % (3499605)------------------------------
% 4.84/1.66 % (3499568)Success in time 0.652 s
% 4.84/1.66 % Vampire exiting
%------------------------------------------------------------------------------