%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM687^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 08:19:18 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM687^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n014.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 12:39:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.19/0.27 % (2594430)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (2594437)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3741366016_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (2594438)% WARNING: option uhcvi not known.
% 0.19/0.27 % (2594438)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3710702056:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (2594441)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3777664968:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (2594439)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2037333348:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (2594440)dis+10_1_sil=32000:sp=arity:random_seed=4100795157:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (2594443)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1165999929:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (2594438)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (2594442)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3003000611:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (2594441)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (2594438)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (2594445)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1355946877:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (2594441) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2594430-2594441"...
% 0.19/0.27 % (2594438) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2594430-2594438"...
% 0.19/0.27 % (2594442) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2594430-2594442"...
% 0.19/0.27 % (2594440) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2594430-2594440"...
% 0.19/0.27 % (2594441)...printing done.
% 0.19/0.27 % (2594443) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2594430-2594443"...
% 0.19/0.27 % (2594441)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% 0.19/0.27 thf(type_def_5, type, nat: $tType).
% 0.19/0.27 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.27 thf(func_def_0, type, x: nat).
% 0.19/0.27 thf(func_def_1, type, y: nat).
% 0.19/0.27 thf(func_def_2, type, z: nat).
% 0.19/0.27 thf(func_def_3, type, u: nat).
% 0.19/0.27 thf(func_def_4, type, more: (nat > nat > $o)).
% 0.19/0.27 thf(func_def_6, type, pl: (nat > nat > nat)).
% 0.19/0.27 thf(func_def_9, type, vNOT: ($o > $o)).
% 0.19/0.27 thf(f1,axiom,(
% 0.19/0.27 ~(more @ x @ y) => (x = y)),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',m)).
% 0.19/0.27 thf(f2,axiom,(
% 0.19/0.27 (more @ z @ u)),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',n)).
% 0.19/0.27 thf(f4,axiom,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((X0 = X1) => ((more @ X2 @ X3) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz19g)).
% 0.19/0.27 thf(f5,axiom,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((more @ X0 @ X1) => ((more @ X2 @ X3) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz21)).
% 0.19/0.27 thf(f6,conjecture,(
% 0.19/0.27 (more @ (pl @ x @ z) @ (pl @ y @ u))),
% 0.19/0.27 file('/export/starexec/sandbox/benchmark/theBenchmark.p',satz22a)).
% 0.19/0.27 thf(f7,negated_conjecture,(
% 0.19/0.27 ~(more @ (pl @ x @ z) @ (pl @ y @ u))),
% 0.19/0.27 inference(negated_conjecture,[status(cth)],[f6])).
% 0.19/0.27 thf(f8,plain,(
% 0.19/0.27 ~(more @ x @ y) => (x = y)),
% 0.19/0.27 inference(rectify,[],[f1])).
% 0.19/0.27 thf(f9,plain,(
% 0.19/0.27 ~ (((more @ x @ y)) = $true) => (x = y)),
% 0.19/0.27 inference(fool_elimination,[],[f8])).
% 0.19/0.27 thf(f10,plain,(
% 0.19/0.27 (more @ z @ u)),
% 0.19/0.27 inference(rectify,[],[f2])).
% 0.19/0.27 thf(f11,plain,(
% 0.19/0.27 (((more @ z @ u)) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f10])).
% 0.19/0.27 thf(f14,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((X0 = X1) => ((more @ X2 @ X3) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))))),
% 0.19/0.27 inference(rectify,[],[f4])).
% 0.19/0.27 thf(f15,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((X0 = X1) => ((((more @ X2 @ X3)) = $true) => (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f14])).
% 0.19/0.27 thf(f16,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((more @ X0 @ X1) => ((more @ X2 @ X3) => (more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))))),
% 0.19/0.27 inference(rectify,[],[f5])).
% 0.19/0.27 thf(f17,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((((more @ X0 @ X1)) = $true) => ((((more @ X2 @ X3)) = $true) => (((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true)))),
% 0.19/0.27 inference(fool_elimination,[],[f16])).
% 0.19/0.27 thf(f18,plain,(
% 0.19/0.27 ~(more @ (pl @ x @ z) @ (pl @ y @ u))),
% 0.19/0.27 inference(rectify,[],[f7])).
% 0.19/0.27 thf(f19,plain,(
% 0.19/0.27 ~ (((more @ (pl @ x @ z) @ (pl @ y @ u))) = $true)),
% 0.19/0.27 inference(fool_elimination,[],[f18])).
% 0.19/0.27 thf(f20,plain,(
% 0.19/0.27 (((more @ x @ y)) != $true) => (x = y)),
% 0.19/0.27 inference(flattening,[],[f9])).
% 0.19/0.27 thf(f22,plain,(
% 0.19/0.27 (((more @ (pl @ x @ z) @ (pl @ y @ u))) != $true)),
% 0.19/0.27 inference(flattening,[],[f19])).
% 0.19/0.27 thf(f23,plain,(
% 0.19/0.27 (x = y) | (((more @ x @ y)) = $true)),
% 0.19/0.27 inference(ennf_transformation,[],[f20])).
% 0.19/0.27 thf(f25,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true)) | (X0 != X1))),
% 0.19/0.27 inference(ennf_transformation,[],[f15])).
% 0.19/0.27 thf(f26,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true) | (X0 != X1))),
% 0.19/0.27 inference(flattening,[],[f25])).
% 0.19/0.27 thf(f27,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : (((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true)) | (((more @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(ennf_transformation,[],[f17])).
% 0.19/0.27 thf(f28,plain,(
% 0.19/0.27 ! [X0 : nat,X1 : nat,X2 : nat,X3 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true) | (((more @ X0 @ X1)) != $true))),
% 0.19/0.27 inference(flattening,[],[f27])).
% 0.19/0.27 thf(f29,plain,(
% 0.19/0.27 (x = y) | (((more @ x @ y)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f23])).
% 0.19/0.27 thf(f30,plain,(
% 0.19/0.27 (((more @ z @ u)) = $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f11])).
% 0.19/0.27 thf(f32,plain,(
% 0.19/0.27 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true) | (X0 != X1)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f26])).
% 0.19/0.27 thf(f33,plain,(
% 0.19/0.27 ( ! [X2 : nat,X3 : nat,X0 : nat,X1 : nat] : ((((more @ (pl @ X0 @ X2) @ (pl @ X1 @ X3))) = $true) | (((more @ X2 @ X3)) != $true) | (((more @ X0 @ X1)) != $true)) )),
% 0.19/0.27 inference(cnf_transformation,[],[f28])).
% 0.19/0.27 thf(f34,plain,(
% 0.19/0.27 (((more @ (pl @ x @ z) @ (pl @ y @ u))) != $true)),
% 0.19/0.27 inference(cnf_transformation,[],[f22])).
% 0.19/0.27 thf(f36,definition,(
% 0.19/0.27 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.27 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.27 thf(f38,plain,(
% 0.19/0.27 ( ! [X2 : nat,X3 : nat,X1 : nat] : (($true = ((more @ (pl @ X1 @ X2) @ (pl @ X1 @ X3)))) | (((more @ X2 @ X3)) != $true)) )),
% 0.19/0.27 inference(equality_resolution,[],[f32])).
% 0.19/0.27 thf(f40,definition,(
% 0.19/0.27 spl0_1 <=> (((more @ x @ y)) = $true)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.19/0.27 thf(f42,plain,(
% 0.19/0.27 (((more @ x @ y)) = $true) | ~spl0_1),
% 0.19/0.27 inference(avatar_component_clause,[],[f40])).
% 0.19/0.27 thf(f44,definition,(
% 0.19/0.27 spl0_2 <=> (x = y)),
% 0.19/0.27 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.19/0.27 thf(f46,plain,(
% 0.19/0.27 (x = y) | ~spl0_2),
% 0.19/0.27 inference(avatar_component_clause,[],[f44])).
% 0.19/0.27 thf(f47,plain,(
% 0.19/0.27 spl0_1 | spl0_2),
% 0.19/0.27 inference(avatar_split_clause,[],[f29,f44,f40])).
% 0.19/0.27 thf(f51,plain,(
% 0.19/0.27 ($true != $true) | (((more @ (pl @ x @ z) @ (pl @ y @ u))) = $false)),
% 0.19/0.27 inference(constrained_superposition,[],[f34,f36])).
% 0.19/0.27 thf(f53,plain,(
% 0.19/0.27 (((more @ (pl @ x @ z) @ (pl @ y @ u))) = $false)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f51])).
% 0.19/0.27 thf(f58,plain,(
% 0.19/0.27 ($false = ((more @ (pl @ x @ z) @ (pl @ x @ u)))) | ~spl0_2),
% 0.19/0.27 inference(forward_demodulation,[],[f53,f46])).
% 0.19/0.27 thf(f64,plain,(
% 0.19/0.27 ($true = $false) | (((more @ z @ u)) != $true) | ~spl0_2),
% 0.19/0.27 inference(constrained_superposition,[],[f38,f58])).
% 0.19/0.27 thf(f69,plain,(
% 0.19/0.27 (((more @ z @ u)) != $true) | ~spl0_2),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f64])).
% 0.19/0.27 thf(f74,plain,(
% 0.19/0.27 $false | ~spl0_2),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f69,f30])).
% 0.19/0.27 thf(f75,plain,(
% 0.19/0.27 ~spl0_2),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f74])).
% 0.19/0.27 thf(f79,plain,(
% 0.19/0.27 ($true = $false) | (((more @ z @ u)) != $true) | (((more @ x @ y)) != $true)),
% 0.19/0.27 inference(constrained_superposition,[],[f33,f53])).
% 0.19/0.27 thf(f84,plain,(
% 0.19/0.27 (((more @ z @ u)) != $true) | (((more @ x @ y)) != $true)),
% 0.19/0.27 inference(trivial_inequality_removal,[],[f79])).
% 0.19/0.27 thf(f87,plain,(
% 0.19/0.27 (((more @ x @ y)) != $true)),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f84,f30])).
% 0.19/0.27 thf(f92,plain,(
% 0.19/0.27 $false | ~spl0_1),
% 0.19/0.27 inference(forward_subsumption_resolution,[],[f87,f42])).
% 0.19/0.27 thf(f93,plain,(
% 0.19/0.27 ~spl0_1),
% 0.19/0.27 inference(avatar_contradiction_clause,[],[f92])).
% 0.19/0.27 cnf(s1, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f47])).
% 0.19/0.27 cnf(s4, plain, ~spl0_2, inference(sat_conversion,[],[f75])).
% 0.19/0.27 cnf(s7, plain, ~spl0_1, inference(sat_conversion,[],[f93])).
% 0.19/0.27 cnf(s8, plain, $false, inference(rat,[],[s1,s4,s7])).
% 0.19/0.27 thf(f94,plain,(
% 0.19/0.27 $false),
% 0.19/0.27 inference(avatar_sat_refutation,[],[s8])).
% 0.19/0.27 % SZS output end Proof for theBenchmark
% 0.19/0.27 % (2594441)------------------------------
% 0.19/0.27 % (2594441)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (2594441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (2594441)CaDiCaL version: 2.1.3
% 0.19/0.27 % (2594441)Termination reason: Refutation
% 0.19/0.27 % (2594441)Time elapsed: 0.004 s
% 0.19/0.27 % (2594441)Peak memory usage: 12 MB
% 0.19/0.27 % (2594441)Instructions burned: 5 (million)
% 0.19/0.27 % (2594430)Success in time 0.051 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------