%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM727^1 : TPTP v9.3.1. Released v3.7.0.
% 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 : Wed Sep 30 08:18:41 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 42 ( 41 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 324 ( 17 ~; 3 |; 0 &; 302 @)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 2 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 40 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
frac: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
x: frac ).
thf(func_def_1,type,
y: frac ).
thf(func_def_2,type,
z: frac ).
thf(func_def_3,type,
ts: nat > nat > nat ).
thf(func_def_4,type,
num: frac > nat ).
thf(func_def_5,type,
den: frac > nat ).
thf(f1,axiom,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(f2,axiom,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f) ).
thf(f3,axiom,
! [X1: nat,X0: nat,X2: nat] :
( ( ( ts @ X0 @ X2 )
= ( ts @ X1 @ X2 ) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz33b) ).
thf(f4,axiom,
! [X1: nat,X0: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz29) ).
thf(f5,axiom,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ ( ts @ X0 @ X1 ) @ X2 )
= ( ts @ X0 @ ( ts @ X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz31) ).
thf(f6,conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',satz39) ).
thf(f7,negated_conjecture,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
thf(f8,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( ts @ ( ts @ X1 @ X2 ) @ X0 )
= ( ts @ X1 @ ( ts @ X2 @ X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f9,plain,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(flattening,[],[f7]) ).
thf(f10,plain,
! [X0: nat,X2: nat,X1: nat] :
( ( ( ts @ X0 @ X2 )
= ( ts @ X1 @ X2 ) )
=> ( X0 = X1 ) ),
inference(rectify,[],[f3]) ).
thf(f11,plain,
! [X2: nat,X1: nat,X0: nat] :
( ( ( ts @ X0 @ X2 )
!= ( ts @ X1 @ X2 ) )
| ( X0 = X1 ) ),
inference(ennf_transformation,[],[f10]) ).
thf(f12,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(rectify,[],[f4]) ).
thf(f13,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ts @ X1 @ ( ts @ X0 @ X2 ) )
= ( ts @ ( ts @ X1 @ X0 ) @ X2 ) ),
inference(rectify,[],[f8]) ).
thf(f14,plain,
! [X0: nat,X1: nat,X2: nat] :
( ( ( ts @ X1 @ X0 )
!= ( ts @ X2 @ X0 ) )
| ( X1 = X2 ) ),
inference(rectify,[],[f11]) ).
thf(f15,plain,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( num @ z ) @ ( den @ y ) ) ),
inference(cnf_transformation,[],[f2]) ).
thf(f16,plain,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( num @ z ) @ ( den @ x ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f17,plain,
! [X0: nat,X1: nat] :
( ( ts @ X0 @ X1 )
= ( ts @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f12]) ).
thf(f18,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( num @ y ) @ ( den @ x ) ) ),
inference(cnf_transformation,[],[f1]) ).
thf(f19,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ X1 @ ( ts @ X0 @ X2 ) )
= ( ts @ ( ts @ X1 @ X0 ) @ X2 ) ),
inference(cnf_transformation,[],[f13]) ).
thf(f20,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ( ts @ X1 @ X0 )
!= ( ts @ X2 @ X0 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[],[f14]) ).
thf(f21,plain,
( ( ts @ ( num @ x ) @ ( den @ y ) )
= ( ts @ ( den @ x ) @ ( num @ y ) ) ),
inference(backward_demodulation,[],[f18,f17]) ).
thf(f22,plain,
( ( ts @ ( num @ y ) @ ( den @ z ) )
= ( ts @ ( den @ y ) @ ( num @ z ) ) ),
inference(forward_demodulation,[],[f15,f17]) ).
thf(f23,plain,
( ( ts @ ( num @ x ) @ ( den @ z ) )
!= ( ts @ ( den @ x ) @ ( num @ z ) ) ),
inference(forward_demodulation,[],[f16,f17]) ).
thf(f24,plain,
( ( ts @ ( den @ x ) @ ( num @ y ) )
= ( ts @ ( den @ y ) @ ( num @ x ) ) ),
inference(forward_demodulation,[],[f21,f17]) ).
thf(f25,plain,
( ( ts @ ( den @ z ) @ ( num @ y ) )
= ( ts @ ( den @ y ) @ ( num @ z ) ) ),
inference(forward_demodulation,[],[f22,f17]) ).
thf(f26,plain,
( ( ts @ ( den @ x ) @ ( num @ z ) )
!= ( ts @ ( den @ z ) @ ( num @ x ) ) ),
inference(forward_demodulation,[],[f23,f17]) ).
thf(f27,plain,
! [X0: nat] :
( ( ts @ ( ts @ ( den @ x ) @ ( num @ z ) ) @ X0 )
!= ( ts @ ( ts @ ( den @ z ) @ ( num @ x ) ) @ X0 ) ),
inference(unit_resulting_resolution,[],[f20,f26]) ).
thf(f36,plain,
! [X0: nat] :
( ( ts @ ( ts @ ( den @ x ) @ ( num @ z ) ) @ X0 )
!= ( ts @ ( den @ z ) @ ( ts @ ( num @ x ) @ X0 ) ) ),
inference(forward_demodulation,[],[f27,f19]) ).
thf(f38,plain,
! [X0: nat] :
( ( ts @ ( den @ z ) @ ( ts @ ( num @ x ) @ X0 ) )
!= ( ts @ ( den @ x ) @ ( ts @ ( num @ z ) @ X0 ) ) ),
inference(forward_demodulation,[],[f36,f19]) ).
thf(f44,plain,
! [X0: nat] :
( ( ts @ ( den @ x ) @ ( ts @ ( num @ z ) @ X0 ) )
!= ( ts @ ( den @ z ) @ ( ts @ X0 @ ( num @ x ) ) ) ),
inference(constrained_superposition,[],[f38,f17]) ).
thf(f58,plain,
( ( ts @ ( den @ x ) @ ( ts @ ( num @ z ) @ ( den @ y ) ) )
!= ( ts @ ( den @ z ) @ ( ts @ ( den @ x ) @ ( num @ y ) ) ) ),
inference(constrained_superposition,[],[f44,f24]) ).
thf(f60,plain,
( ( ts @ ( den @ x ) @ ( ts @ ( den @ y ) @ ( num @ z ) ) )
!= ( ts @ ( den @ z ) @ ( ts @ ( den @ x ) @ ( num @ y ) ) ) ),
inference(forward_demodulation,[],[f58,f17]) ).
thf(f63,plain,
( ( ts @ ( den @ x ) @ ( ts @ ( den @ z ) @ ( num @ y ) ) )
!= ( ts @ ( den @ z ) @ ( ts @ ( den @ x ) @ ( num @ y ) ) ) ),
inference(forward_demodulation,[],[f60,f25]) ).
thf(f81,plain,
! [X2: nat,X0: nat,X1: nat] :
( ( ts @ X0 @ ( ts @ X1 @ X2 ) )
= ( ts @ X2 @ ( ts @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f17,f19]) ).
thf(f84,plain,
( ( ts @ ( den @ x ) @ ( ts @ ( num @ y ) @ ( den @ z ) ) )
!= ( ts @ ( den @ x ) @ ( ts @ ( den @ z ) @ ( num @ y ) ) ) ),
inference(backward_demodulation,[],[f63,f81]) ).
thf(f88,plain,
( ( ts @ ( den @ x ) @ ( ts @ ( den @ z ) @ ( num @ y ) ) )
!= ( ts @ ( den @ x ) @ ( ts @ ( den @ z ) @ ( num @ y ) ) ) ),
inference(forward_demodulation,[],[f84,f17]) ).
thf(f89,plain,
$false,
inference(trivial_inequality_removal,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM727^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n015.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 : Tue Sep 29 12:48:48 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.30 % (3469919)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (3469924)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3659933586:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (3469926)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=469641882:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (3469925)lrs+10_16_si=on:nwc=1.5:random_seed=2898400266:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (3469928)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=518931993:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (3469927)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3091188438:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.30 % (3469926)Instruction limit reached!
% 0.21/0.30 % (3469926)------------------------------
% 0.21/0.30 % (3469926)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3469926)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3469926)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3469926)Termination reason: Instruction limit
% 0.21/0.30 % (3469926)Termination phase: Saturation
% 0.21/0.30 % (3469926)Time elapsed: 0.003 s
% 0.21/0.30 % (3469926)Peak memory usage: 12 MB
% 0.21/0.30 % (3469926)Instructions burned: 5 (million)
% 0.21/0.30 % (3469930)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (3469930)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.30 % (3469929)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3919222973:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (3469925)Instruction limit reached!
% 0.21/0.30 % (3469925)------------------------------
% 0.21/0.30 % (3469925)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3469925)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3469925)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3469925)Termination reason: Instruction limit
% 0.21/0.30 % (3469925)Termination phase: Saturation
% 0.21/0.30 % (3469925)Time elapsed: 0.010 s
% 0.21/0.30 % (3469925)Peak memory usage: 12 MB
% 0.21/0.30 % (3469925)Instructions burned: 19 (million)
% 0.21/0.30 % (3469930)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1881129405:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (3469928)Instruction limit reached!
% 0.21/0.30 % (3469928)------------------------------
% 0.21/0.30 % (3469928)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3469928)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3469928)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3469928)Termination reason: Instruction limit
% 0.21/0.30 % (3469928)Termination phase: Saturation
% 0.21/0.30 % (3469928)Time elapsed: 0.012 s
% 0.21/0.30 % (3469928)Peak memory usage: 11 MB
% 0.21/0.30 % (3469928)Instructions burned: 25 (million)
% 0.21/0.30 % (3469924)Instruction limit reached!
% 0.21/0.30 % (3469924)------------------------------
% 0.21/0.30 % (3469924)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3469924)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3469924)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3469924)Termination reason: Instruction limit
% 0.21/0.30 % (3469924)Termination phase: Saturation
% 0.21/0.30 % (3469924)Time elapsed: 0.021 s
% 0.21/0.30 % (3469924)Peak memory usage: 12 MB
% 0.21/0.30 % (3469924)Instructions burned: 88 (million)
% 0.21/0.30 % (3469936)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2807913451:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.30 % (3469941)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1161720701:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.30 % (3469936)Instruction limit reached!
% 0.21/0.30 % (3469936)------------------------------
% 0.21/0.30 % (3469936)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3469936)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3469936)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3469936)Termination reason: Instruction limit
% 0.21/0.30 % (3469936)Termination phase: Saturation
% 0.21/0.30 % (3469936)Time elapsed: 0.004 s
% 0.21/0.30 % (3469936)Peak memory usage: 12 MB
% 0.21/0.30 % (3469936)Instructions burned: 6 (million)
% 0.21/0.30 % (3469941) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3469919-3469941"...
% 0.21/0.30 % (3469940)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.30 % (3469941)...printing done.
% 0.21/0.30 % (3469941)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (3469941)------------------------------
% 0.21/0.30 % (3469941)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (3469941)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (3469941)CaDiCaL version: 2.1.3
% 0.21/0.30 % (3469941)Termination reason: Refutation
% 0.21/0.30 % (3469941)Time elapsed: 0.003 s
% 0.21/0.30 % (3469941)Peak memory usage: 12 MB
% 0.21/0.30 % (3469941)Instructions burned: 11 (million)
% 0.21/0.30 % (3469919)Success in time 0.058 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------