%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 01:21:11 PM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 57 ( 18 unt; 2 def)
% Number of atoms : 140 ( 18 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 138 ( 55 ~; 52 |; 23 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 79 ( 1 sgn 66 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( less_than(X0,X1)
& ~ less_than(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(f5,axiom,
! [X0] : less_than(bottom,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',bottom_smallest) ).
fof(f38,axiom,
! [X0,X1] : findmin_cpq_res(triple(X0,create_slb,X1)) = bottom,
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax50) ).
fof(f39,axiom,
! [X0,X1,X2,X3] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(f41,axiom,
! [X0] : removemin_cpq_res(X0) = findmin_cpq_res(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax53) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( contains_slb(X0,X1)
& strictly_less_than(X1,X2) )
=> ( pair_in_list(update_slb(X0,X2),X1,X2)
| ? [X3] :
( pair_in_list(update_slb(X0,X2),X1,X3)
& less_than(X2,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_l45) ).
fof(f43,conjecture,
! [X0,X1,X2,X3] :
( ( contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) )
=> ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
| ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(f44,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) )
=> ( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
| ? [X4] :
( pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
& less_than(findmin_pqp_res(X0),X4) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f52,plain,
! [X0,X1,X2] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
inference(rectify,[],[f39]) ).
fof(f79,plain,
! [X0,X1,X2] :
( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0)
| create_slb = X1 ),
inference(ennf_transformation,[],[f52]) ).
fof(f80,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ? [X3] :
( pair_in_list(update_slb(X0,X2),X1,X3)
& less_than(X2,X3) )
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f81,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ? [X3] :
( pair_in_list(update_slb(X0,X2),X1,X3)
& less_than(X2,X3) )
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
? [X0,X1,X2,X3] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& ! [X4] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
| ~ less_than(findmin_pqp_res(X0),X4) )
& contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f44]) ).
fof(f83,plain,
? [X0,X1,X2,X3] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& ! [X4] :
( ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4)
| ~ less_than(findmin_pqp_res(X0),X4) )
& contains_slb(X1,X3)
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2))) ),
inference(flattening,[],[f82]) ).
fof(f84,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) )
& ( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
| ~ strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f85,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| ~ less_than(X0,X1)
| less_than(X1,X0) )
& ( ( less_than(X0,X1)
& ~ less_than(X1,X0) )
| ~ strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f84]) ).
fof(f92,plain,
! [X0,X1,X2] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ( pair_in_list(update_slb(X0,X2),X1,sK0(X0,X1,X2))
& less_than(X2,sK0(X0,X1,X2)) )
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f81]) ).
fof(f93,plain,
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
& ! [X4] :
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4)
| ~ less_than(findmin_pqp_res(sK1),X4) )
& contains_slb(sK2,sK4)
& strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f83]) ).
fof(f97,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ less_than(X1,X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f100,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f140,plain,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f141,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f79]) ).
fof(f143,plain,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
inference(cnf_transformation,[],[f41]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ contains_slb(X0,X1)
| less_than(X2,sK0(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ contains_slb(X0,X1)
| pair_in_list(update_slb(X0,X2),X1,sK0(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f146,plain,
strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))),
inference(cnf_transformation,[],[f93]) ).
fof(f147,plain,
contains_slb(sK2,sK4),
inference(cnf_transformation,[],[f93]) ).
fof(f148,plain,
! [X4] :
( ~ less_than(findmin_pqp_res(sK1),X4)
| ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4) ),
inference(cnf_transformation,[],[f93]) ).
fof(f149,plain,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
inference(definition_unfolding,[],[f140,f143]) ).
fof(f153,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(definition_unfolding,[],[f141,f143]) ).
fof(f154,plain,
strictly_less_than(sK4,removemin_cpq_res(triple(sK1,sK2,sK3))),
inference(definition_unfolding,[],[f146,f143]) ).
fof(f159,plain,
~ less_than(removemin_cpq_res(triple(sK1,sK2,sK3)),sK4),
inference(resolution,[],[f97,f154]) ).
fof(f256,plain,
( strictly_less_than(sK4,findmin_pqp_res(sK1))
| create_slb = sK2 ),
inference(superposition,[],[f154,f153]) ).
fof(f271,definition,
( spl5_1
<=> create_slb = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f273,plain,
( create_slb = sK2
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f301,definition,
( spl5_8
<=> strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
fof(f303,plain,
( strictly_less_than(sK4,findmin_pqp_res(sK1))
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f304,plain,
( spl5_1
| spl5_8 ),
inference(avatar_split_clause,[],[f256,f301,f271]) ).
fof(f422,plain,
! [X0] :
( ~ strictly_less_than(sK4,X0)
| pair_in_list(update_slb(sK2,X0),sK4,X0)
| less_than(X0,sK0(sK2,sK4,X0)) ),
inference(resolution,[],[f144,f147]) ).
fof(f491,plain,
! [X0] :
( ~ strictly_less_than(sK4,X0)
| pair_in_list(update_slb(sK2,X0),sK4,X0)
| pair_in_list(update_slb(sK2,X0),sK4,sK0(sK2,sK4,X0)) ),
inference(resolution,[],[f145,f147]) ).
fof(f590,plain,
( ~ less_than(removemin_cpq_res(triple(sK1,create_slb,sK3)),sK4)
| ~ spl5_1 ),
inference(superposition,[],[f159,f273]) ).
fof(f613,plain,
( ~ less_than(bottom,sK4)
| ~ spl5_1 ),
inference(forward_demodulation,[],[f590,f152]) ).
fof(f621,plain,
( $false
| ~ spl5_1 ),
inference(forward_subsumption_resolution,[],[f613,f100]) ).
fof(f622,plain,
~ spl5_1,
inference(avatar_contradiction_clause,[],[f621]) ).
fof(f623,plain,
( pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
| less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ spl5_8 ),
inference(resolution,[],[f303,f422]) ).
fof(f627,plain,
( less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f623,f149]) ).
fof(f629,plain,
( pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
| pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ spl5_8 ),
inference(resolution,[],[f491,f303]) ).
fof(f630,plain,
( pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f629,f149]) ).
fof(f647,plain,
( ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ spl5_8 ),
inference(resolution,[],[f627,f148]) ).
fof(f656,plain,
( $false
| ~ spl5_8 ),
inference(forward_subsumption_resolution,[],[f647,f630]) ).
fof(f657,plain,
~ spl5_8,
inference(avatar_contradiction_clause,[],[f656]) ).
cnf(s7,plain,
( spl5_1
| spl5_8 ),
inference(sat_conversion,[],[f304]) ).
cnf(s15,plain,
~ spl5_1,
inference(sat_conversion,[],[f622]) ).
cnf(s18,plain,
~ spl5_8,
inference(sat_conversion,[],[f657]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s7,s18,s15]) ).
fof(f658,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.19 % Computer : n010.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 10:51:32 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.22 Running first-order model finding
% 0.07/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (1845205)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (1845215)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1774220135:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.27 % (1845211)% WARNING: option uhcvi not known.
% 0.20/0.27 % (1845210)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4125650564_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.27 % (1845212)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3504901878:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.27 % (1845211)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2537971450:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.27 % (1845213)dis+10_1_sil=32000:sp=arity:random_seed=2030011449:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.27 % (1845214)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4113712383:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (1845216)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=701859789:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.27 % (1845215) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1845205-1845215"...
% 0.20/0.27 % (1845215)...printing done.
% 0.20/0.27 % (1845215)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1845215)------------------------------
% 0.20/0.27 % (1845215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1845215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1845215)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1845215)Termination reason: Refutation
% 0.20/0.27 % (1845215)Time elapsed: 0.010 s
% 0.20/0.27 % (1845215)Peak memory usage: 13 MB
% 0.20/0.27 % (1845215)Instructions burned: 26 (million)
% 0.20/0.27 % (1845205)Success in time 0.036 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------