%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : LCL977_1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:01:20 PM UTC 2026
% Result : Theorem 0.22s 0.50s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL977_1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.41 % Computer : n005.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Sun Sep 27 17:09:31 UTC 2026
% 0.17/0.41 % CPUTime :
% 0.17/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.17/0.45 Running first-order model finding
% 0.17/0.45 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
% 0.22/0.50 % (28024)Will run a generic schedule for satisfiability detection.
% 0.22/0.50 % (28032)dis+10_1_sil=32000:sp=arity:random_seed=335977944:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.22/0.50 % (28030)% WARNING: option uhcvi not known.
% 0.22/0.50 % (28029)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3945440023_2999 on theBenchmark for (2999ds/0Mi)
% 0.22/0.50 % (28031)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1355440272:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.22/0.50 % (28030)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3829444817:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.22/0.50 % (28032) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-28024-28032"...
% 0.22/0.50 % (28033)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=193006292:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.22/0.50 % (28035)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=4123980498:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.22/0.50 % (28034)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1002829806:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.22/0.50 % Detected minimum model sizes of [1,1]
% 0.22/0.50 % Detected maximum model sizes of [max,2]
% 0.22/0.50 % TRYING [1,1]
% 0.22/0.50 % TRYING [1,2]
% 0.22/0.50 % (28032)...printing done.
% 0.22/0.50 % TRYING [2,2]
% 0.22/0.50 % TRYING [3,2]
% 0.22/0.50 % (28032)Refutation found. Thanks to Tanya!
% 0.22/0.50 % SZS status Theorem for theBenchmark
% 0.22/0.50 % SZS output start Proof for theBenchmark
% 0.22/0.50 tff(func_def_3, type, bG0: $o > $o).
% 0.22/0.50 tff(func_def_4, type, bG1: $o > $o).
% 0.22/0.50 tff(func_def_5, type, bG2: ($i * $i * $i) > $o).
% 0.22/0.50 tff(func_def_6, type, bG3: ($i * $i) > $o).
% 0.22/0.50 tff(pred_def_1, type, imply: ($o * $o) > $o).
% 0.22/0.50 tff(f1,axiom,(
% 0.22/0.50 ! [X0 : $o,X1 : $o] : (imply(X0,X1) = ~X0 | X1)),
% 0.22/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',imply_definition)).
% 0.22/0.50 tff(f2,axiom,(
% 0.22/0.50 ! [X0 : $i,X1 : $i] : (p(X0,X1) => f(X0) = X1)),
% 0.22/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_impl)).
% 0.22/0.50 tff(f3,conjecture,(
% 0.22/0.50 ! [X0 : $i,X1 : $i,X2 : $i] : imply(p(X0,X1) & p(X0,X2),X1 = X2)),
% 0.22/0.50 file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_conjecture)).
% 0.22/0.50 tff(f4,negated_conjecture,(
% 0.22/0.50 ~ ! [X0 : $i,X1 : $i,X2 : $i] : imply(p(X0,X1) & p(X0,X2),X1 = X2)),
% 0.22/0.50 inference(negated_conjecture,[status(cth)],[f3])).
% 0.22/0.50 tff(f5,plain,(
% 0.22/0.50 ! [X0 : $o,X1 : $o] : (imply(X0,X1) = ~X0 | X1)),
% 0.22/0.50 inference(rectify,[],[f1])).
% 0.22/0.50 tff(f6,definition,(
% 0.22/0.50 ! [X0 : $o] : (($true = X0) <=> ($true = bG0(X0)))),
% 0.22/0.50 introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition])).
% 0.22/0.50 tff(f7,definition,(
% 0.22/0.50 ! [X1 : $o] : (($true = X1) <=> ($true = bG1(X1)))),
% 0.22/0.50 introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition])).
% 0.22/0.50 tff(f8,plain,(
% 0.22/0.50 ! [X0 : $o,X1 : $o] : (imply(bG0(X0),bG1(X1)) <=> (~ ($true = X0) | ($true = X1)))),
% 0.22/0.50 inference(fool_elimination,[],[f5,f7,f6])).
% 0.22/0.50 tff(f9,definition,(
% 0.22/0.50 ! [X1 : $i,X0 : $i,X2 : $i] : ((p(X0,X1) & p(X0,X2)) <=> ($true = bG2(X1,X0,X2)))),
% 0.22/0.50 introduced(definition,[new_symbols(definition,[bG2])],[fool_formula_definition])).
% 0.22/0.50 tff(f10,definition,(
% 0.22/0.50 ! [X2 : $i,X1 : $i] : (X1 = X2 <=> ($true = bG3(X2,X1)))),
% 0.22/0.50 introduced(definition,[new_symbols(definition,[bG3])],[fool_formula_definition])).
% 0.22/0.50 tff(f11,plain,(
% 0.22/0.50 ~ ! [X0 : $i,X1 : $i,X2 : $i] : imply(bG2(X1,X0,X2),bG3(X2,X1))),
% 0.22/0.50 inference(fool_elimination,[],[f4,f10,f9])).
% 0.22/0.50 tff(f12,plain,(
% 0.22/0.50 ! [X0 : $i,X1 : $i] : (X0 = X1 <=> ($true = bG3(X0,X1)))),
% 0.22/0.50 inference(rectify,[],[f10])).
% 0.22/0.50 tff(f13,plain,(
% 0.22/0.50 ! [X0 : $i,X1 : $i,X2 : $i] : ((p(X1,X0) & p(X1,X2)) <=> ($true = bG2(X0,X1,X2)))),
% 0.22/0.50 inference(rectify,[],[f9])).
% 0.22/0.50 tff(f14,plain,(
% 0.22/0.50 ! [X0 : $o] : (($true = X0) <=> ($true = bG1(X0)))),
% 0.22/0.50 inference(rectify,[],[f7])).
% 0.22/0.50 tff(f15,plain,(
% 0.22/0.50 ! [X0 : $o,X1 : $o] : (imply(bG0(X0),bG1(X1)) <=> (($true != X0) | ($true = X1)))),
% 0.22/0.50 inference(flattening,[],[f8])).
% 0.22/0.50 tff(f16,plain,(
% 0.22/0.50 ! [X0 : $i,X1 : $i] : (f(X0) = X1 | ~p(X0,X1))),
% 0.22/0.50 inference(ennf_transformation,[],[f2])).
% 0.22/0.50 tff(f17,plain,(
% 0.22/0.50 ? [X0 : $i,X1 : $i,X2 : $i] : ~imply(bG2(X1,X0,X2),bG3(X2,X1))),
% 0.22/0.50 inference(ennf_transformation,[],[f11])).
% 0.22/0.50 tff(f18,plain,(
% 0.22/0.50 ! [X0 : $i,X1 : $i] : ((X0 = X1 | ($true != bG3(X0,X1))) & (($true = bG3(X0,X1)) | X0 != X1))),
% 0.22/0.50 inference(nnf_transformation,[],[f12])).
% 0.22/0.50 tff(f19,plain,(
% 0.22/0.50 ! [X0 : $i,X1 : $i,X2 : $i] : (((p(X1,X0) & p(X1,X2)) | ($true != bG2(X0,X1,X2))) & (($true = bG2(X0,X1,X2)) | (~p(X1,X0) | ~p(X1,X2))))),
% 0.22/0.50 inference(nnf_transformation,[],[f13])).
% 0.22/0.50 tff(f20,plain,(
% 0.22/0.50 ! [X0 : $i,X1 : $i,X2 : $i] : (((p(X1,X0) & p(X1,X2)) | ($true != bG2(X0,X1,X2))) & (($true = bG2(X0,X1,X2)) | ~p(X1,X0) | ~p(X1,X2)))),
% 0.22/0.50 inference(flattening,[],[f19])).
% 0.22/0.50 tff(f21,plain,(
% 0.22/0.50 ! [X0 : $o] : ((($true = X0) | ($true != bG1(X0))) & (($true = bG1(X0)) | ($true != X0)))),
% 0.22/0.50 inference(nnf_transformation,[],[f14])).
% 0.22/0.50 tff(f22,plain,(
% 0.22/0.50 ! [X0 : $o] : ((($true = X0) | ($true != bG0(X0))) & (($true = bG0(X0)) | ($true != X0)))),
% 0.22/0.50 inference(nnf_transformation,[],[f6])).
% 0.22/0.50 tff(f23,plain,(
% 0.22/0.50 ! [X0 : $o,X1 : $o] : ((imply(bG0(X0),bG1(X1)) | (($true = X0) & ($true != X1))) & ((($true != X0) | ($true = X1)) | ~imply(bG0(X0),bG1(X1))))),
% 0.22/0.50 inference(nnf_transformation,[],[f15])).
% 0.22/0.50 tff(f24,plain,(
% 0.22/0.50 ! [X0 : $o,X1 : $o] : ((imply(bG0(X0),bG1(X1)) | (($true = X0) & ($true != X1))) & (($true != X0) | ($true = X1) | ~imply(bG0(X0),bG1(X1))))),
% 0.22/0.50 inference(flattening,[],[f23])).
% 0.22/0.50 tff(f25,plain,(
% 0.22/0.50 ~imply(bG2(sK5,sK4,sK6),bG3(sK6,sK5))),
% 0.22/0.50 inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5,sK6]),skolemize(X0,sK4),skolemize(X1,sK5),skolemize(X2,sK6)],[f17])).
% 0.22/0.50 tff(f26,plain,(
% 0.22/0.50 ( ! [X0 : $i,X1 : $i] : (($true = bG3(X0,X1)) | X0 != X1) )),
% 0.22/0.50 inference(cnf_transformation,[],[f18])).
% 0.22/0.50 tff(f29,plain,(
% 0.22/0.50 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != bG2(X0,X1,X2)) | p(X1,X2)) )),
% 0.22/0.50 inference(cnf_transformation,[],[f20])).
% 0.22/0.50 tff(f30,plain,(
% 0.22/0.50 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != bG2(X0,X1,X2)) | p(X1,X0)) )),
% 0.22/0.50 inference(cnf_transformation,[],[f20])).
% 0.22/0.50 tff(f31,plain,(
% 0.22/0.50 ( ! [X0 : $o] : (($true = bG1(X0)) | ($true != X0)) )),
% 0.22/0.50 inference(cnf_transformation,[],[f21])).
% 0.22/0.50 tff(f32,plain,(
% 0.22/0.50 ( ! [X0 : $o] : (($true != bG1(X0)) | ($true = X0)) )),
% 0.22/0.50 inference(cnf_transformation,[],[f21])).
% 0.22/0.51 tff(f33,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true = bG0(X0)) | ($true != X0)) )),
% 0.22/0.51 inference(cnf_transformation,[],[f22])).
% 0.22/0.51 tff(f34,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true != bG0(X0)) | ($true = X0)) )),
% 0.22/0.51 inference(cnf_transformation,[],[f22])).
% 0.22/0.51 tff(f36,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : (imply(bG0(X0),bG1(X1)) | ($true != X1)) )),
% 0.22/0.51 inference(cnf_transformation,[],[f24])).
% 0.22/0.51 tff(f37,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : (imply(bG0(X0),bG1(X1)) | ($true = X0)) )),
% 0.22/0.51 inference(cnf_transformation,[],[f24])).
% 0.22/0.51 tff(f38,plain,(
% 0.22/0.51 ( ! [X0 : $i,X1 : $i] : (~p(X0,X1) | f(X0) = X1) )),
% 0.22/0.51 inference(cnf_transformation,[],[f16])).
% 0.22/0.51 tff(f39,plain,(
% 0.22/0.51 ~imply(bG2(sK5,sK4,sK6),bG3(sK6,sK5))),
% 0.22/0.51 inference(cnf_transformation,[],[f25])).
% 0.22/0.51 tff(f40,definition,(
% 0.22/0.51 ($true != $false)),
% 0.22/0.51 introduced(theory,[fool_distinctness_axiom])).
% 0.22/0.51 tff(f41,definition,(
% 0.22/0.51 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.22/0.51 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.22/0.51 tff(f42,plain,(
% 0.22/0.51 ( ! [X1 : $i] : (($true = bG3(X1,X1))) )),
% 0.22/0.51 inference(equality_resolution,[],[f26])).
% 0.22/0.51 tff(f43,plain,(
% 0.22/0.51 ($true = bG1($true))),
% 0.22/0.51 inference(equality_resolution,[],[f31])).
% 0.22/0.51 tff(f44,plain,(
% 0.22/0.51 ($true = bG0($true))),
% 0.22/0.51 inference(equality_resolution,[],[f33])).
% 0.22/0.51 tff(f45,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (imply(bG0(X0),bG1($true))) )),
% 0.22/0.51 inference(equality_resolution,[],[f36])).
% 0.22/0.51 tff(f47,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (imply(bG0(X0),$true)) )),
% 0.22/0.51 inference(forward_demodulation,[],[f45,f43])).
% 0.22/0.51 tff(f48,plain,(
% 0.22/0.51 imply($true,$true)),
% 0.22/0.51 inference(superposition,[],[f47,f44])).
% 0.22/0.51 tff(f49,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : ((X0 = X1) | ($false = X1) | ($false = X0)) )),
% 0.22/0.51 inference(superposition,[],[f41,f41])).
% 0.22/0.51 tff(f50,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : (imply(bG0(X1),X0) | ($false = X0)) )),
% 0.22/0.51 inference(superposition,[],[f47,f41])).
% 0.22/0.51 tff(f51,plain,(
% 0.22/0.51 ( ! [X0 : $o] : ((bG0(X0) = X0) | ($false = X0)) )),
% 0.22/0.51 inference(superposition,[],[f44,f41])).
% 0.22/0.51 tff(f55,plain,(
% 0.22/0.51 ~imply($true,bG3(sK6,sK5)) | (bG2(sK5,sK4,sK6) = $false)),
% 0.22/0.51 inference(superposition,[],[f39,f41])).
% 0.22/0.51 tff(f56,plain,(
% 0.22/0.51 ~imply(bG2(sK5,sK4,sK6),$true) | (bG3(sK6,sK5) = $false)),
% 0.22/0.51 inference(superposition,[],[f39,f41])).
% 0.22/0.51 tff(f59,definition,(
% 0.22/0.51 spl7_1 <=> (bG3(sK6,sK5) = $false)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.22/0.51 tff(f61,plain,(
% 0.22/0.51 (bG3(sK6,sK5) = $false) | ~spl7_1),
% 0.22/0.51 inference(avatar_component_clause,[],[f59])).
% 0.22/0.51 tff(f63,definition,(
% 0.22/0.51 spl7_2 <=> imply(bG2(sK5,sK4,sK6),$true)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.22/0.51 tff(f65,plain,(
% 0.22/0.51 ~imply(bG2(sK5,sK4,sK6),$true) | spl7_2),
% 0.22/0.51 inference(avatar_component_clause,[],[f63])).
% 0.22/0.51 tff(f66,plain,(
% 0.22/0.51 spl7_1 | ~spl7_2),
% 0.22/0.51 inference(avatar_split_clause,[],[f56,f63,f59])).
% 0.22/0.51 tff(f68,definition,(
% 0.22/0.51 spl7_3 <=> (bG2(sK5,sK4,sK6) = $false)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.22/0.51 tff(f69,plain,(
% 0.22/0.51 (bG2(sK5,sK4,sK6) != $false) | spl7_3),
% 0.22/0.51 inference(avatar_component_clause,[],[f68])).
% 0.22/0.51 tff(f70,plain,(
% 0.22/0.51 (bG2(sK5,sK4,sK6) = $false) | ~spl7_3),
% 0.22/0.51 inference(avatar_component_clause,[],[f68])).
% 0.22/0.51 tff(f72,definition,(
% 0.22/0.51 spl7_4 <=> imply($true,bG3(sK6,sK5))),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 0.22/0.51 tff(f74,plain,(
% 0.22/0.51 ~imply($true,bG3(sK6,sK5)) | spl7_4),
% 0.22/0.51 inference(avatar_component_clause,[],[f72])).
% 0.22/0.51 tff(f75,plain,(
% 0.22/0.51 spl7_3 | ~spl7_4),
% 0.22/0.51 inference(avatar_split_clause,[],[f55,f72,f68])).
% 0.22/0.51 tff(f80,definition,(
% 0.22/0.51 spl7_6 <=> imply($true,$true)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.22/0.51 tff(f84,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (~imply(X0,bG3(sK6,sK5)) | ($false = X0)) ) | spl7_4),
% 0.22/0.51 inference(superposition,[],[f74,f41])).
% 0.22/0.51 tff(f85,plain,(
% 0.22/0.51 ~imply($true,$true) | (bG3(sK6,sK5) = $false) | spl7_4),
% 0.22/0.51 inference(superposition,[],[f74,f41])).
% 0.22/0.51 tff(f86,plain,(
% 0.22/0.51 spl7_1 | ~spl7_6 | spl7_4),
% 0.22/0.51 inference(avatar_split_clause,[],[f85,f72,f80,f59])).
% 0.22/0.51 tff(f87,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | (bG1(X0) = $false)) )),
% 0.22/0.51 inference(superposition,[],[f32,f41])).
% 0.22/0.51 tff(f88,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true = X0) | (bG1(X0) = $false)) )),
% 0.22/0.51 inference(trivial_inequality_removal,[],[f87])).
% 0.22/0.51 tff(f90,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (~imply(bG2(sK5,sK4,sK6),X0) | ($false = X0)) ) | spl7_2),
% 0.22/0.51 inference(superposition,[],[f65,f41])).
% 0.22/0.51 tff(f92,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | (bG0(X0) = $false)) )),
% 0.22/0.51 inference(superposition,[],[f34,f41])).
% 0.22/0.51 tff(f93,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true = X0) | (bG0(X0) = $false)) )),
% 0.22/0.51 inference(trivial_inequality_removal,[],[f92])).
% 0.22/0.51 tff(f112,definition,(
% 0.22/0.51 spl7_8 <=> ! [X0 : $o] : (($true = X0) | (bG0(X0) = $false))),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition])).
% 0.22/0.51 tff(f113,plain,(
% 0.22/0.51 ( ! [X0 : $o] : ((bG0(X0) = $false) | ($true = X0)) ) | ~spl7_8),
% 0.22/0.51 inference(avatar_component_clause,[],[f112])).
% 0.22/0.51 tff(f123,definition,(
% 0.22/0.51 spl7_10 <=> ! [X0 : $o] : (($true = X0) | (bG1(X0) = $false))),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition])).
% 0.22/0.51 tff(f124,plain,(
% 0.22/0.51 ( ! [X0 : $o] : ((bG1(X0) = $false) | ($true = X0)) ) | ~spl7_10),
% 0.22/0.51 inference(avatar_component_clause,[],[f123])).
% 0.22/0.51 tff(f136,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (~imply($false,X0) | ($false = X0)) ) | (spl7_2 | ~spl7_3)),
% 0.22/0.51 inference(superposition,[],[f90,f70])).
% 0.22/0.51 tff(f139,plain,(
% 0.22/0.51 ~imply($false,bG3(sK6,sK5)) | ~spl7_3),
% 0.22/0.51 inference(superposition,[],[f39,f70])).
% 0.22/0.51 tff(f143,plain,(
% 0.22/0.51 ~imply($false,$false) | (~spl7_1 | ~spl7_3)),
% 0.22/0.51 inference(forward_demodulation,[],[f139,f61])).
% 0.22/0.51 tff(f145,plain,(
% 0.22/0.51 spl7_6),
% 0.22/0.51 inference(avatar_split_clause,[],[f48,f80])).
% 0.22/0.51 tff(f161,definition,(
% 0.22/0.51 spl7_12 <=> ! [X0 : $o] : ($true = X0)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition])).
% 0.22/0.51 tff(f162,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true = X0)) ) | ~spl7_12),
% 0.22/0.51 inference(avatar_component_clause,[],[f161])).
% 0.22/0.51 tff(f164,definition,(
% 0.22/0.51 spl7_13 <=> ! [X1 : $o] : imply($false,bG1(X1))),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_13])],[avatar_definition])).
% 0.22/0.51 tff(f165,plain,(
% 0.22/0.51 ( ! [X1 : $o] : (imply($false,bG1(X1))) ) | ~spl7_13),
% 0.22/0.51 inference(avatar_component_clause,[],[f164])).
% 0.22/0.51 tff(f169,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (imply($true,X0) | ($false = X0)) )),
% 0.22/0.51 inference(superposition,[],[f50,f44])).
% 0.22/0.51 tff(f172,definition,(
% 0.22/0.51 spl7_14 <=> ! [X1 : $o] : (imply($true,X1) | ($false = X1))),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_14])],[avatar_definition])).
% 0.22/0.51 tff(f173,plain,(
% 0.22/0.51 ( ! [X1 : $o] : (imply($true,X1) | ($false = X1)) ) | ~spl7_14),
% 0.22/0.51 inference(avatar_component_clause,[],[f172])).
% 0.22/0.51 tff(f175,plain,(
% 0.22/0.51 spl7_14),
% 0.22/0.51 inference(avatar_split_clause,[],[f169,f172])).
% 0.22/0.51 tff(f180,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (imply(X0,$true) | ($false = X0)) )),
% 0.22/0.51 inference(superposition,[],[f47,f51])).
% 0.22/0.51 tff(f202,plain,(
% 0.22/0.51 spl7_10),
% 0.22/0.51 inference(avatar_split_clause,[],[f88,f123])).
% 0.22/0.51 tff(f209,plain,(
% 0.22/0.51 spl7_8),
% 0.22/0.51 inference(avatar_split_clause,[],[f93,f112])).
% 0.22/0.51 tff(f213,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : (imply($false,X1) | ($false = X1) | ($true = X0)) ) | ~spl7_8),
% 0.22/0.51 inference(superposition,[],[f50,f113])).
% 0.22/0.51 tff(f214,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : (imply($false,bG1(X1)) | ($true = X0) | ($true = X0)) ) | ~spl7_8),
% 0.22/0.51 inference(superposition,[],[f37,f113])).
% 0.22/0.51 tff(f218,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : (imply($false,bG1(X1)) | ($true = X0)) ) | ~spl7_8),
% 0.22/0.51 inference(duplicate_literal_removal,[],[f214])).
% 0.22/0.51 tff(f223,plain,(
% 0.22/0.51 spl7_12 | spl7_13 | ~spl7_8),
% 0.22/0.51 inference(avatar_split_clause,[],[f218,f112,f164,f161])).
% 0.22/0.51 tff(f224,plain,(
% 0.22/0.51 ( ! [X0 : $o,X1 : $o] : (($false = X1) | ($true = X0)) ) | (spl7_2 | ~spl7_3 | ~spl7_8)),
% 0.22/0.51 inference(forward_subsumption_resolution,[],[f213,f136])).
% 0.22/0.51 tff(f227,definition,(
% 0.22/0.51 spl7_15 <=> ! [X1 : $o] : ($false = X1)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_15])],[avatar_definition])).
% 0.22/0.51 tff(f228,plain,(
% 0.22/0.51 ( ! [X1 : $o] : (($false = X1)) ) | ~spl7_15),
% 0.22/0.51 inference(avatar_component_clause,[],[f227])).
% 0.22/0.51 tff(f229,plain,(
% 0.22/0.51 spl7_12 | spl7_15 | spl7_2 | ~spl7_3 | ~spl7_8),
% 0.22/0.51 inference(avatar_split_clause,[],[f224,f112,f68,f63,f227,f161])).
% 0.22/0.51 tff(f272,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (~imply($true,X0) | ($false = X0)) ) | (spl7_2 | ~spl7_12)),
% 0.22/0.51 inference(superposition,[],[f90,f162])).
% 0.22/0.51 tff(f278,plain,(
% 0.22/0.51 ($true = $false) | (~spl7_1 | ~spl7_12)),
% 0.22/0.51 inference(superposition,[],[f61,f162])).
% 0.22/0.51 tff(f284,plain,(
% 0.22/0.51 $false | (~spl7_1 | ~spl7_12)),
% 0.22/0.51 inference(trivial_inequality_removal,[],[f278])).
% 0.22/0.51 tff(f285,plain,(
% 0.22/0.51 ~spl7_1 | ~spl7_12),
% 0.22/0.51 inference(avatar_contradiction_clause,[],[f284])).
% 0.22/0.51 tff(f299,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($false = X0)) ) | (spl7_2 | ~spl7_12 | ~spl7_14)),
% 0.22/0.51 inference(forward_subsumption_resolution,[],[f272,f173])).
% 0.22/0.51 tff(f307,plain,(
% 0.22/0.51 spl7_15 | spl7_2 | ~spl7_12 | ~spl7_14),
% 0.22/0.51 inference(avatar_split_clause,[],[f299,f172,f161,f63,f227])).
% 0.22/0.51 tff(f630,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (imply($false,$false) | ($true = X0)) ) | (~spl7_10 | ~spl7_13)),
% 0.22/0.51 inference(superposition,[],[f165,f124])).
% 0.22/0.51 tff(f645,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true = X0)) ) | (~spl7_1 | ~spl7_3 | ~spl7_10 | ~spl7_13)),
% 0.22/0.51 inference(forward_subsumption_resolution,[],[f630,f143])).
% 0.22/0.51 tff(f647,plain,(
% 0.22/0.51 spl7_12 | ~spl7_1 | ~spl7_3 | ~spl7_10 | ~spl7_13),
% 0.22/0.51 inference(avatar_split_clause,[],[f645,f164,f123,f68,f59,f161])).
% 0.22/0.51 tff(f649,definition,(
% 0.22/0.51 spl7_26 <=> ! [X0 : $o] : ((bG2(sK5,sK4,sK6) = X0) | ($false = X0))),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_26])],[avatar_definition])).
% 0.22/0.51 tff(f650,plain,(
% 0.22/0.51 ( ! [X0 : $o] : ((bG2(sK5,sK4,sK6) = X0) | ($false = X0)) ) | ~spl7_26),
% 0.22/0.51 inference(avatar_component_clause,[],[f649])).
% 0.22/0.51 tff(f678,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($false != $false) | (bG2(sK5,sK4,sK6) = X0) | ($false = X0)) ) | spl7_3),
% 0.22/0.51 inference(superposition,[],[f69,f49])).
% 0.22/0.51 tff(f682,plain,(
% 0.22/0.51 ( ! [X0 : $o] : ((bG2(sK5,sK4,sK6) = X0) | ($false = X0)) ) | spl7_3),
% 0.22/0.51 inference(trivial_inequality_removal,[],[f678])).
% 0.22/0.51 tff(f684,plain,(
% 0.22/0.51 spl7_26 | spl7_3),
% 0.22/0.51 inference(avatar_split_clause,[],[f682,f68,f649])).
% 0.22/0.51 tff(f712,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true != X0) | p(sK4,sK5) | ($false = X0)) ) | ~spl7_26),
% 0.22/0.51 inference(superposition,[],[f30,f650])).
% 0.22/0.51 tff(f713,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($true != X0) | p(sK4,sK6) | ($false = X0)) ) | ~spl7_26),
% 0.22/0.51 inference(superposition,[],[f29,f650])).
% 0.22/0.51 tff(f752,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (p(sK4,sK6) | ($false = X0)) ) | ~spl7_26),
% 0.22/0.51 inference(forward_subsumption_resolution,[],[f713,f41])).
% 0.22/0.51 tff(f753,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (p(sK4,sK5) | ($false = X0)) ) | ~spl7_26),
% 0.22/0.51 inference(forward_subsumption_resolution,[],[f712,f41])).
% 0.22/0.51 tff(f757,definition,(
% 0.22/0.51 spl7_31 <=> p(sK4,sK6)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_31])],[avatar_definition])).
% 0.22/0.51 tff(f759,plain,(
% 0.22/0.51 p(sK4,sK6) | ~spl7_31),
% 0.22/0.51 inference(avatar_component_clause,[],[f757])).
% 0.22/0.51 tff(f760,plain,(
% 0.22/0.51 spl7_15 | spl7_31 | ~spl7_26),
% 0.22/0.51 inference(avatar_split_clause,[],[f752,f649,f757,f227])).
% 0.22/0.51 tff(f762,definition,(
% 0.22/0.51 spl7_32 <=> p(sK4,sK5)),
% 0.22/0.51 introduced(definition,[new_symbols(definition,[spl7_32])],[avatar_definition])).
% 0.22/0.51 tff(f764,plain,(
% 0.22/0.51 p(sK4,sK5) | ~spl7_32),
% 0.22/0.51 inference(avatar_component_clause,[],[f762])).
% 0.22/0.51 tff(f765,plain,(
% 0.22/0.51 spl7_15 | spl7_32 | ~spl7_26),
% 0.22/0.51 inference(avatar_split_clause,[],[f753,f649,f762,f227])).
% 0.22/0.51 tff(f777,plain,(
% 0.22/0.51 ($false != $false) | ~spl7_15),
% 0.22/0.51 inference(superposition,[],[f40,f228])).
% 0.22/0.51 tff(f829,plain,(
% 0.22/0.51 $false | ~spl7_15),
% 0.22/0.51 inference(trivial_inequality_removal,[],[f777])).
% 0.22/0.51 tff(f830,plain,(
% 0.22/0.51 ~spl7_15),
% 0.22/0.51 inference(avatar_contradiction_clause,[],[f829])).
% 0.22/0.51 tff(f850,plain,(
% 0.22/0.51 sK6 = f(sK4) | ~spl7_31),
% 0.22/0.51 inference(resolution,[],[f759,f38])).
% 0.22/0.51 tff(f858,plain,(
% 0.22/0.51 sK5 = f(sK4) | ~spl7_32),
% 0.22/0.51 inference(resolution,[],[f764,f38])).
% 0.22/0.51 tff(f871,plain,(
% 0.22/0.51 sK5 = sK6 | (~spl7_31 | ~spl7_32)),
% 0.22/0.51 inference(superposition,[],[f858,f850])).
% 0.22/0.51 tff(f893,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (~imply(X0,bG3(sK5,sK5)) | ($false = X0)) ) | (spl7_4 | ~spl7_31 | ~spl7_32)),
% 0.22/0.51 inference(superposition,[],[f84,f871])).
% 0.22/0.51 tff(f898,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (~imply(X0,$true) | ($false = X0)) ) | (spl7_4 | ~spl7_31 | ~spl7_32)),
% 0.22/0.51 inference(forward_demodulation,[],[f893,f42])).
% 0.22/0.51 tff(f904,plain,(
% 0.22/0.51 ( ! [X0 : $o] : (($false = X0)) ) | (spl7_4 | ~spl7_31 | ~spl7_32)),
% 0.22/0.51 inference(forward_subsumption_resolution,[],[f898,f180])).
% 0.22/0.51 tff(f907,plain,(
% 0.22/0.51 spl7_15 | spl7_4 | ~spl7_31 | ~spl7_32),
% 0.22/0.51 inference(avatar_split_clause,[],[f904,f762,f757,f72,f227])).
% 0.22/0.51 cnf(s1, plain, spl7_1 | ~spl7_2, inference(sat_conversion,[],[f66])).
% 0.22/0.51 cnf(s2, plain, spl7_3 | ~spl7_4, inference(sat_conversion,[],[f75])).
% 0.22/0.51 cnf(s4, plain, spl7_1 | spl7_4 | ~spl7_6, inference(sat_conversion,[],[f86])).
% 0.22/0.51 cnf(s10, plain, spl7_6, inference(sat_conversion,[],[f145])).
% 0.22/0.51 cnf(s16, plain, spl7_14, inference(sat_conversion,[],[f175])).
% 0.22/0.51 cnf(s18, plain, spl7_10, inference(sat_conversion,[],[f202])).
% 0.22/0.51 cnf(s19, plain, spl7_8, inference(sat_conversion,[],[f209])).
% 0.22/0.51 cnf(s20, plain, ~spl7_8 | spl7_12 | spl7_13, inference(sat_conversion,[],[f223])).
% 0.22/0.51 cnf(s22, plain, spl7_2 | ~spl7_3 | ~spl7_8 | spl7_12 | spl7_15, inference(sat_conversion,[],[f229])).
% 0.22/0.51 cnf(s24, plain, ~spl7_1 | ~spl7_12, inference(sat_conversion,[],[f285])).
% 0.22/0.51 cnf(s29, plain, spl7_2 | ~spl7_12 | ~spl7_14 | spl7_15, inference(sat_conversion,[],[f307])).
% 0.22/0.51 cnf(s59, plain, ~spl7_1 | ~spl7_3 | ~spl7_10 | spl7_12 | ~spl7_13, inference(sat_conversion,[],[f647])).
% 0.22/0.51 cnf(s67, plain, spl7_3 | spl7_26, inference(sat_conversion,[],[f684])).
% 0.22/0.51 cnf(s79, plain, spl7_15 | ~spl7_26 | spl7_31, inference(sat_conversion,[],[f760])).
% 0.22/0.51 cnf(s80, plain, spl7_15 | ~spl7_26 | spl7_32, inference(sat_conversion,[],[f765])).
% 0.22/0.51 cnf(s85, plain, ~spl7_15, inference(sat_conversion,[],[f830])).
% 0.22/0.51 cnf(s94, plain, spl7_4 | spl7_15 | ~spl7_31 | ~spl7_32, inference(sat_conversion,[],[f907])).
% 0.22/0.51 cnf(s95, plain, ~spl7_26 | spl7_32, inference(rat,[],[s80,s85])).
% 0.22/0.51 cnf(s96, plain, ~spl7_26 | spl7_31, inference(rat,[],[s79,s85])).
% 0.22/0.51 cnf(s97, plain, spl7_2 | ~spl7_12 | ~spl7_14, inference(rat,[],[s29,s85])).
% 0.22/0.51 cnf(s99, plain, spl7_2 | ~spl7_3 | ~spl7_8 | spl7_12, inference(rat,[],[s22,s85])).
% 0.22/0.51 cnf(s101, plain, spl7_1 | spl7_4, inference(rat,[],[s4,s10])).
% 0.22/0.51 cnf(s102, plain, spl7_1, inference(rat,[],[s99,s97,s2,s1,s101,s19,s16])).
% 0.22/0.51 cnf(s103, plain, ~spl7_12, inference(rat,[],[s24,s102])).
% 0.22/0.51 cnf(s107, plain, spl7_13, inference(rat,[],[s20,s19,s103])).
% 0.22/0.51 cnf(s108, plain, ~spl7_3, inference(rat,[],[s59,s107,s102,s18,s103])).
% 0.22/0.51 cnf(s110, plain, spl7_26, inference(rat,[],[s67,s108])).
% 0.22/0.51 cnf(s112, plain, ~spl7_4, inference(rat,[],[s2,s108])).
% 0.22/0.51 cnf(s113, plain, spl7_32, inference(rat,[],[s95,s110])).
% 0.22/0.51 cnf(s114, plain, spl7_31, inference(rat,[],[s96,s110])).
% 0.22/0.51 cnf(s116, plain, $false, inference(rat,[],[s94,s113,s85,s114,s112])).
% 0.22/0.51 tff(f908,plain,(
% 0.22/0.51 $false),
% 0.22/0.51 inference(avatar_sat_refutation,[],[s116])).
% 0.22/0.51 % SZS output end Proof for theBenchmark
% 0.22/0.51 % (28032)------------------------------
% 0.22/0.51 % (28032)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.51 % (28032)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.51 % (28032)CaDiCaL version: 2.1.3
% 0.22/0.51 % (28032)Termination reason: Refutation
% 0.22/0.51 % (28032)Time elapsed: 0.015 s
% 0.22/0.51 % (28032)Peak memory usage: 12 MB
% 0.22/0.51 % (28032)Instructions burned: 25 (million)
% 0.22/0.51 % (28024)Success in time 0.039 s
% 0.22/0.51 % Vampire exiting
%------------------------------------------------------------------------------