%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU709_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:54:24 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU709_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 05:48:21 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.48 % (3284322)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (3284336)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2186880481:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (3284332)% WARNING: option uhcvi not known.
% 0.18/0.48 % (3284333)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2178643209:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (3284332)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=773281100:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (3284335)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3203964047:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (3284337)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2692893500:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (3284334)dis+10_1_sil=32000:sp=arity:random_seed=2114901677:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (3284331)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=151265554_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (3284336) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3284322-3284336"...
% 0.18/0.48 % Detected minimum model sizes of [1,1]
% 0.18/0.48 % Detected maximum model sizes of [max,2]
% 0.18/0.48 % TRYING [1,1]
% 0.18/0.48 % (3284336)...printing done.
% 0.18/0.48 % TRYING [1,2]
% 0.18/0.48 % TRYING [2,2]
% 0.18/0.48 % (3284336)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% 0.18/0.48 tff(func_def_2, type, if: ($i * $o * $i * $i) > $i).
% 0.18/0.48 tff(func_def_5, type, bG0: $o > $o).
% 0.18/0.48 tff(func_def_6, type, bG1: $o > $o).
% 0.18/0.48 tff(func_def_7, type, bG2: $o > $o).
% 0.18/0.48 tff(func_def_9, type, sK4: $o).
% 0.18/0.48 tff(f1,axiom,(
% 0.18/0.48 (setadjoinIL = ! [X0 : $i,X1 : $i] : in(X0,setadjoin(X0,X1)))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL)).
% 0.18/0.48 tff(f3,axiom,(
% 0.18/0.48 (secondinupair = ! [X0 : $i,X1 : $i] : in(X1,setadjoin(X0,setadjoin(X1,emptyset))))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair)).
% 0.18/0.48 tff(f4,axiom,(
% 0.18/0.48 (iftrue = ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (X1 => if(X0,X1,X2,X3) = X2))))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrue)).
% 0.18/0.48 tff(f5,axiom,(
% 0.18/0.48 (iffalse = ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (~X1 => if(X0,X1,X2,X3) = X3))))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iffalse)).
% 0.18/0.48 tff(f6,conjecture,(
% 0.18/0.48 setadjoinIL => (in__Cong => (secondinupair => (iftrue => (iffalse => ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => in(if(X0,X1,X2,X3),setadjoin(X2,setadjoin(X3,emptyset)))))))))),
% 0.18/0.48 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iftrueorfalse)).
% 0.18/0.48 tff(f7,negated_conjecture,(
% 0.18/0.48 ~(setadjoinIL => (in__Cong => (secondinupair => (iftrue => (iffalse => ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => in(if(X0,X1,X2,X3),setadjoin(X2,setadjoin(X3,emptyset))))))))))),
% 0.18/0.48 inference(negated_conjecture,[status(cth)],[f6])).
% 0.18/0.48 tff(f8,plain,(
% 0.18/0.48 setadjoinIL <=> ! [X0 : $i,X1 : $i] : in(X0,setadjoin(X0,X1))),
% 0.18/0.48 inference(fool_elimination,[],[f1])).
% 0.18/0.48 tff(f10,plain,(
% 0.18/0.48 secondinupair <=> ! [X0 : $i,X1 : $i] : in(X1,setadjoin(X0,setadjoin(X1,emptyset)))),
% 0.18/0.48 inference(fool_elimination,[],[f3])).
% 0.18/0.48 tff(f11,plain,(
% 0.18/0.48 (iftrue = ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (X1 => if(X0,X1,X2,X3) = X2))))),
% 0.18/0.48 inference(rectify,[],[f4])).
% 0.18/0.48 tff(f12,definition,(
% 0.18/0.48 ! [X1 : $o] : (($true = X1) <=> ($true = bG0(X1)))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition])).
% 0.18/0.48 tff(f13,plain,(
% 0.18/0.48 iftrue <=> ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (($true = X1) => if(X0,bG0(X1),X2,X3) = X2)))),
% 0.18/0.48 inference(fool_elimination,[],[f11,f12])).
% 0.18/0.48 tff(f14,plain,(
% 0.18/0.48 (iffalse = ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (~X1 => if(X0,X1,X2,X3) = X3))))),
% 0.18/0.48 inference(rectify,[],[f5])).
% 0.18/0.48 tff(f15,definition,(
% 0.18/0.48 ! [X1 : $o] : (($true = X1) <=> ($true = bG1(X1)))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition])).
% 0.18/0.48 tff(f16,plain,(
% 0.18/0.48 iffalse <=> ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (~ ($true = X1) => if(X0,bG1(X1),X2,X3) = X3)))),
% 0.18/0.48 inference(fool_elimination,[],[f14,f15])).
% 0.18/0.48 tff(f17,plain,(
% 0.18/0.48 ~(setadjoinIL => (in__Cong => (secondinupair => (iftrue => (iffalse => ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => in(if(X0,X1,X2,X3),setadjoin(X2,setadjoin(X3,emptyset))))))))))),
% 0.18/0.48 inference(rectify,[],[f7])).
% 0.18/0.48 tff(f18,definition,(
% 0.18/0.48 ! [X1 : $o] : (($true = X1) <=> ($true = bG2(X1)))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[bG2])],[fool_formula_definition])).
% 0.18/0.48 tff(f19,plain,(
% 0.18/0.48 ~(setadjoinIL => (in__Cong => (secondinupair => (iftrue => (iffalse => ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => in(if(X0,bG2(X1),X2,X3),setadjoin(X2,setadjoin(X3,emptyset))))))))))),
% 0.18/0.48 inference(fool_elimination,[],[f17,f18])).
% 0.18/0.48 tff(f20,plain,(
% 0.18/0.48 ! [X0 : $o] : (($true = X0) <=> ($true = bG2(X0)))),
% 0.18/0.48 inference(rectify,[],[f18])).
% 0.18/0.48 tff(f21,plain,(
% 0.18/0.48 ! [X0 : $o] : (($true = X0) <=> ($true = bG1(X0)))),
% 0.18/0.48 inference(rectify,[],[f15])).
% 0.18/0.48 tff(f22,plain,(
% 0.18/0.48 ! [X0 : $o] : (($true = X0) <=> ($true = bG0(X0)))),
% 0.18/0.48 inference(rectify,[],[f12])).
% 0.18/0.48 tff(f23,plain,(
% 0.18/0.48 iffalse <=> ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (($true != X1) => if(X0,bG1(X1),X2,X3) = X3)))),
% 0.18/0.48 inference(flattening,[],[f16])).
% 0.18/0.48 tff(f24,plain,(
% 0.18/0.48 iffalse => ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (($true != X1) => if(X0,bG1(X1),X2,X3) = X3)))),
% 0.18/0.48 inference(unused_predicate_definition_removal,[],[f23])).
% 0.18/0.48 tff(f25,plain,(
% 0.18/0.48 iftrue => ! [X0 : $i,X1 : $o,X2 : $i] : (in(X2,X0) => ! [X3 : $i] : (in(X3,X0) => (($true = X1) => if(X0,bG0(X1),X2,X3) = X2)))),
% 0.18/0.48 inference(unused_predicate_definition_removal,[],[f13])).
% 0.18/0.48 tff(f26,plain,(
% 0.18/0.48 secondinupair => ! [X0 : $i,X1 : $i] : in(X1,setadjoin(X0,setadjoin(X1,emptyset)))),
% 0.18/0.48 inference(unused_predicate_definition_removal,[],[f10])).
% 0.18/0.48 tff(f28,plain,(
% 0.18/0.48 setadjoinIL => ! [X0 : $i,X1 : $i] : in(X0,setadjoin(X0,X1))),
% 0.18/0.48 inference(unused_predicate_definition_removal,[],[f8])).
% 0.18/0.48 tff(f29,plain,(
% 0.18/0.48 ! [X0 : $i,X1 : $i] : in(X0,setadjoin(X0,X1)) | ~setadjoinIL),
% 0.18/0.48 inference(ennf_transformation,[],[f28])).
% 0.18/0.48 tff(f31,plain,(
% 0.18/0.48 ! [X0 : $i,X1 : $i] : in(X1,setadjoin(X0,setadjoin(X1,emptyset))) | ~secondinupair),
% 0.18/0.48 inference(ennf_transformation,[],[f26])).
% 0.18/0.48 tff(f32,plain,(
% 0.18/0.48 ! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : ((if(X0,bG0(X1),X2,X3) = X2 | ($true != X1)) | ~in(X3,X0)) | ~in(X2,X0)) | ~iftrue),
% 0.18/0.48 inference(ennf_transformation,[],[f25])).
% 0.18/0.48 tff(f33,plain,(
% 0.18/0.48 ! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : (if(X0,bG0(X1),X2,X3) = X2 | ($true != X1) | ~in(X3,X0)) | ~in(X2,X0)) | ~iftrue),
% 0.18/0.48 inference(flattening,[],[f32])).
% 0.18/0.48 tff(f34,plain,(
% 0.18/0.48 ! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : ((if(X0,bG1(X1),X2,X3) = X3 | ($true = X1)) | ~in(X3,X0)) | ~in(X2,X0)) | ~iffalse),
% 0.18/0.48 inference(ennf_transformation,[],[f24])).
% 0.18/0.48 tff(f35,plain,(
% 0.18/0.48 ! [X0 : $i,X1 : $o,X2 : $i] : (! [X3 : $i] : (if(X0,bG1(X1),X2,X3) = X3 | ($true = X1) | ~in(X3,X0)) | ~in(X2,X0)) | ~iffalse),
% 0.18/0.48 inference(flattening,[],[f34])).
% 0.18/0.48 tff(f36,plain,(
% 0.18/0.48 ((((? [X0 : $i,X1 : $o,X2 : $i] : (? [X3 : $i] : (~in(if(X0,bG2(X1),X2,X3),setadjoin(X2,setadjoin(X3,emptyset))) & in(X3,X0)) & in(X2,X0)) & iffalse) & iftrue) & secondinupair) & in__Cong) & setadjoinIL),
% 0.18/0.48 inference(ennf_transformation,[],[f19])).
% 0.18/0.48 tff(f37,plain,(
% 0.18/0.48 ? [X0 : $i,X1 : $o,X2 : $i] : (? [X3 : $i] : (~in(if(X0,bG2(X1),X2,X3),setadjoin(X2,setadjoin(X3,emptyset))) & in(X3,X0)) & in(X2,X0)) & iffalse & iftrue & secondinupair & in__Cong & setadjoinIL),
% 0.18/0.48 inference(flattening,[],[f36])).
% 0.18/0.48 tff(f38,plain,(
% 0.18/0.48 ! [X0 : $o] : ((($true = X0) | ($true != bG2(X0))) & (($true = bG2(X0)) | ($true != X0)))),
% 0.18/0.48 inference(nnf_transformation,[],[f20])).
% 0.18/0.48 tff(f39,plain,(
% 0.18/0.48 ! [X0 : $o] : ((($true = X0) | ($true != bG1(X0))) & (($true = bG1(X0)) | ($true != X0)))),
% 0.18/0.48 inference(nnf_transformation,[],[f21])).
% 0.18/0.48 tff(f40,plain,(
% 0.18/0.48 ! [X0 : $o] : ((($true = X0) | ($true != bG0(X0))) & (($true = bG0(X0)) | ($true != X0)))),
% 0.18/0.48 inference(nnf_transformation,[],[f22])).
% 0.18/0.48 tff(f42,plain,(
% 0.18/0.48 ((~in(if(sK3,bG2(sK4),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) & in(sK6,sK3)) & in(sK5,sK3)) & iffalse & iftrue & secondinupair & in__Cong & setadjoinIL),
% 0.18/0.48 inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6)],[f37])).
% 0.18/0.48 tff(f43,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true != X0) | ($true = bG2(X0))) )),
% 0.18/0.48 inference(cnf_transformation,[],[f38])).
% 0.18/0.48 tff(f44,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true != bG2(X0)) | ($true = X0)) )),
% 0.18/0.48 inference(cnf_transformation,[],[f38])).
% 0.18/0.48 tff(f46,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true != bG1(X0)) | ($true = X0)) )),
% 0.18/0.48 inference(cnf_transformation,[],[f39])).
% 0.18/0.48 tff(f47,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true != X0) | ($true = bG0(X0))) )),
% 0.18/0.48 inference(cnf_transformation,[],[f40])).
% 0.18/0.48 tff(f49,plain,(
% 0.18/0.48 ( ! [X0 : $i,X1 : $i] : (in(X0,setadjoin(X0,X1)) | ~setadjoinIL) )),
% 0.18/0.48 inference(cnf_transformation,[],[f29])).
% 0.18/0.48 tff(f52,plain,(
% 0.18/0.48 ( ! [X0 : $i,X1 : $i] : (in(X1,setadjoin(X0,setadjoin(X1,emptyset))) | ~secondinupair) )),
% 0.18/0.48 inference(cnf_transformation,[],[f31])).
% 0.18/0.48 tff(f53,plain,(
% 0.18/0.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (if(X0,bG0(X1),X2,X3) = X2 | ($true != X1) | ~in(X3,X0) | ~in(X2,X0) | ~iftrue) )),
% 0.18/0.48 inference(cnf_transformation,[],[f33])).
% 0.18/0.48 tff(f54,plain,(
% 0.18/0.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (if(X0,bG1(X1),X2,X3) = X3 | ($true = X1) | ~in(X3,X0) | ~in(X2,X0) | ~iffalse) )),
% 0.18/0.48 inference(cnf_transformation,[],[f35])).
% 0.18/0.48 tff(f55,plain,(
% 0.18/0.48 setadjoinIL),
% 0.18/0.48 inference(cnf_transformation,[],[f42])).
% 0.18/0.48 tff(f57,plain,(
% 0.18/0.48 secondinupair),
% 0.18/0.48 inference(cnf_transformation,[],[f42])).
% 0.18/0.48 tff(f58,plain,(
% 0.18/0.48 iftrue),
% 0.18/0.48 inference(cnf_transformation,[],[f42])).
% 0.18/0.48 tff(f59,plain,(
% 0.18/0.48 iffalse),
% 0.18/0.48 inference(cnf_transformation,[],[f42])).
% 0.18/0.48 tff(f60,plain,(
% 0.18/0.48 in(sK5,sK3)),
% 0.18/0.48 inference(cnf_transformation,[],[f42])).
% 0.18/0.48 tff(f61,plain,(
% 0.18/0.48 in(sK6,sK3)),
% 0.18/0.48 inference(cnf_transformation,[],[f42])).
% 0.18/0.48 tff(f62,plain,(
% 0.18/0.48 ~in(if(sK3,bG2(sK4),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))),
% 0.18/0.48 inference(cnf_transformation,[],[f42])).
% 0.18/0.48 tff(f64,definition,(
% 0.18/0.48 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.18/0.48 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.18/0.48 tff(f65,plain,(
% 0.18/0.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (~in(X3,X0) | ($true = X1) | if(X0,bG1(X1),X2,X3) = X3 | ~in(X2,X0)) )),
% 0.18/0.48 inference(forward_subsumption_resolution,[],[f54,f59])).
% 0.18/0.48 tff(f66,plain,(
% 0.18/0.48 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $o] : (~in(X3,X0) | ($true != X1) | if(X0,bG0(X1),X2,X3) = X2 | ~in(X2,X0)) )),
% 0.18/0.48 inference(forward_subsumption_resolution,[],[f53,f58])).
% 0.18/0.48 tff(f67,plain,(
% 0.18/0.48 ( ! [X0 : $i,X1 : $i] : (in(X1,setadjoin(X0,setadjoin(X1,emptyset)))) )),
% 0.18/0.48 inference(forward_subsumption_resolution,[],[f52,f57])).
% 0.18/0.48 tff(f70,plain,(
% 0.18/0.48 ( ! [X0 : $i,X1 : $i] : (in(X0,setadjoin(X0,X1))) )),
% 0.18/0.48 inference(forward_subsumption_resolution,[],[f49,f55])).
% 0.18/0.48 tff(f76,plain,(
% 0.18/0.48 ( ! [X0 : $o,X1 : $i] : (~in(X1,sK3) | sK6 = if(sK3,bG1(X0),X1,sK6) | ($true = X0)) )),
% 0.18/0.48 inference(resolution,[],[f65,f61])).
% 0.18/0.48 tff(f81,plain,(
% 0.18/0.48 ( ! [X0 : $o,X1 : $i] : (~in(X1,sK3) | if(sK3,bG0(X0),X1,sK6) = X1 | ($true != X0)) )),
% 0.18/0.48 inference(resolution,[],[f66,f61])).
% 0.18/0.48 tff(f88,plain,(
% 0.18/0.48 ~in(if(sK3,bG2($true),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) | (sK4 = $false)),
% 0.18/0.48 inference(superposition,[],[f62,f64])).
% 0.18/0.48 tff(f101,definition,(
% 0.18/0.48 spl7_3 <=> (sK4 = $false)),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.18/0.48 tff(f103,plain,(
% 0.18/0.48 (sK4 = $false) | ~spl7_3),
% 0.18/0.48 inference(avatar_component_clause,[],[f101])).
% 0.18/0.48 tff(f105,definition,(
% 0.18/0.48 spl7_4 <=> in(if(sK3,bG2($true),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 0.18/0.48 tff(f107,plain,(
% 0.18/0.48 ~in(if(sK3,bG2($true),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) | spl7_4),
% 0.18/0.48 inference(avatar_component_clause,[],[f105])).
% 0.18/0.48 tff(f108,plain,(
% 0.18/0.48 spl7_3 | ~spl7_4),
% 0.18/0.48 inference(avatar_split_clause,[],[f88,f105,f101])).
% 0.18/0.48 tff(f111,plain,(
% 0.18/0.48 ($true = bG2($true))),
% 0.18/0.48 inference(equality_resolution,[],[f43])).
% 0.18/0.48 tff(f113,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | (bG2(X0) = $false)) )),
% 0.18/0.48 inference(superposition,[],[f44,f64])).
% 0.18/0.48 tff(f114,plain,(
% 0.18/0.48 ( ! [X0 : $o] : ((bG2(X0) = $false) | ($true = X0)) )),
% 0.18/0.48 inference(trivial_inequality_removal,[],[f113])).
% 0.18/0.48 tff(f119,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true != $true) | ($true = X0) | (bG1(X0) = $false)) )),
% 0.18/0.48 inference(superposition,[],[f46,f64])).
% 0.18/0.48 tff(f120,plain,(
% 0.18/0.48 ( ! [X0 : $o] : ((bG1(X0) = $false) | ($true = X0)) )),
% 0.18/0.48 inference(trivial_inequality_removal,[],[f119])).
% 0.18/0.48 tff(f124,plain,(
% 0.18/0.48 ($true = bG0($true))),
% 0.18/0.48 inference(equality_resolution,[],[f47])).
% 0.18/0.48 tff(f132,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (sK6 = if(sK3,bG1(X0),sK5,sK6) | ($true = X0)) )),
% 0.18/0.48 inference(resolution,[],[f76,f60])).
% 0.18/0.48 tff(f138,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true != X0) | sK5 = if(sK3,bG0(X0),sK5,sK6)) )),
% 0.18/0.48 inference(resolution,[],[f81,f60])).
% 0.18/0.48 tff(f157,plain,(
% 0.18/0.48 ~in(if(sK3,$true,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) | spl7_4),
% 0.18/0.48 inference(superposition,[],[f107,f111])).
% 0.18/0.48 tff(f164,plain,(
% 0.18/0.48 sK5 = if(sK3,bG0($true),sK5,sK6)),
% 0.18/0.48 inference(equality_resolution,[],[f138])).
% 0.18/0.48 tff(f165,plain,(
% 0.18/0.48 sK5 = if(sK3,$true,sK5,sK6)),
% 0.18/0.48 inference(forward_demodulation,[],[f164,f124])).
% 0.18/0.48 tff(f167,plain,(
% 0.18/0.48 ~in(if(sK3,$false,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) | ($true = sK4)),
% 0.18/0.48 inference(superposition,[],[f62,f114])).
% 0.18/0.48 tff(f172,definition,(
% 0.18/0.48 spl7_5 <=> ($true = sK4)),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition])).
% 0.18/0.48 tff(f174,plain,(
% 0.18/0.48 ($true = sK4) | ~spl7_5),
% 0.18/0.48 inference(avatar_component_clause,[],[f172])).
% 0.18/0.48 tff(f176,definition,(
% 0.18/0.48 spl7_6 <=> in(if(sK3,$false,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset)))),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition])).
% 0.18/0.48 tff(f178,plain,(
% 0.18/0.48 ~in(if(sK3,$false,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) | spl7_6),
% 0.18/0.48 inference(avatar_component_clause,[],[f176])).
% 0.18/0.48 tff(f179,plain,(
% 0.18/0.48 spl7_5 | ~spl7_6),
% 0.18/0.48 inference(avatar_split_clause,[],[f167,f176,f172])).
% 0.18/0.48 tff(f186,plain,(
% 0.18/0.48 ~in(sK5,setadjoin(sK5,setadjoin(sK6,emptyset))) | spl7_4),
% 0.18/0.48 inference(forward_demodulation,[],[f157,f165])).
% 0.18/0.48 tff(f188,plain,(
% 0.18/0.48 $false | spl7_4),
% 0.18/0.48 inference(forward_subsumption_resolution,[],[f186,f70])).
% 0.18/0.48 tff(f189,plain,(
% 0.18/0.48 spl7_4),
% 0.18/0.48 inference(avatar_contradiction_clause,[],[f188])).
% 0.18/0.48 tff(f203,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (sK6 = if(sK3,$false,sK5,sK6) | ($true = X0) | ($true = X0)) )),
% 0.18/0.48 inference(superposition,[],[f132,f120])).
% 0.18/0.48 tff(f210,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (sK6 = if(sK3,$false,sK5,sK6) | ($true = X0)) )),
% 0.18/0.48 inference(duplicate_literal_removal,[],[f203])).
% 0.18/0.48 tff(f214,definition,(
% 0.18/0.48 spl7_7 <=> ! [X0 : $o] : ($true = X0)),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition])).
% 0.18/0.48 tff(f215,plain,(
% 0.18/0.48 ( ! [X0 : $o] : (($true = X0)) ) | ~spl7_7),
% 0.18/0.48 inference(avatar_component_clause,[],[f214])).
% 0.18/0.48 tff(f227,definition,(
% 0.18/0.48 spl7_10 <=> sK6 = if(sK3,$false,sK5,sK6)),
% 0.18/0.48 introduced(definition,[new_symbols(definition,[spl7_10])],[avatar_definition])).
% 0.18/0.48 tff(f229,plain,(
% 0.18/0.48 sK6 = if(sK3,$false,sK5,sK6) | ~spl7_10),
% 0.18/0.48 inference(avatar_component_clause,[],[f227])).
% 0.18/0.48 tff(f230,plain,(
% 0.18/0.48 spl7_7 | spl7_10),
% 0.18/0.48 inference(avatar_split_clause,[],[f210,f227,f214])).
% 0.18/0.48 tff(f265,plain,(
% 0.18/0.48 ~in(if(sK3,bG2($true),sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) | ~spl7_7),
% 0.18/0.48 inference(superposition,[],[f62,f215])).
% 0.18/0.48 tff(f275,plain,(
% 0.18/0.48 ~in(if(sK3,$true,sK5,sK6),setadjoin(sK5,setadjoin(sK6,emptyset))) | ~spl7_7),
% 0.18/0.48 inference(forward_demodulation,[],[f265,f111])).
% 0.18/0.48 tff(f286,plain,(
% 0.18/0.48 ~in(sK5,setadjoin(sK5,setadjoin(sK6,emptyset))) | ~spl7_7),
% 0.18/0.48 inference(forward_demodulation,[],[f275,f165])).
% 0.18/0.48 tff(f289,plain,(
% 0.18/0.48 $false | ~spl7_7),
% 0.18/0.48 inference(forward_subsumption_resolution,[],[f286,f70])).
% 0.18/0.48 tff(f290,plain,(
% 0.18/0.48 ~spl7_7),
% 0.18/0.48 inference(avatar_contradiction_clause,[],[f289])).
% 0.18/0.48 tff(f522,plain,(
% 0.18/0.48 ~in(sK6,setadjoin(sK5,setadjoin(sK6,emptyset))) | (spl7_6 | ~spl7_10)),
% 0.18/0.48 inference(superposition,[],[f178,f229])).
% 0.18/0.48 tff(f523,plain,(
% 0.18/0.48 $false | (spl7_6 | ~spl7_10)),
% 0.18/0.48 inference(forward_subsumption_resolution,[],[f522,f67])).
% 0.18/0.48 tff(f524,plain,(
% 0.18/0.48 spl7_6 | ~spl7_10),
% 0.18/0.48 inference(avatar_contradiction_clause,[],[f523])).
% 0.18/0.48 tff(f525,plain,(
% 0.18/0.48 ($true = $false) | (~spl7_3 | ~spl7_5)),
% 0.18/0.48 inference(forward_demodulation,[],[f174,f103])).
% 0.18/0.48 tff(f526,plain,(
% 0.18/0.48 $false | (~spl7_3 | ~spl7_5)),
% 0.18/0.48 inference(trivial_inequality_removal,[],[f525])).
% 0.18/0.48 tff(f527,plain,(
% 0.18/0.48 ~spl7_3 | ~spl7_5),
% 0.18/0.48 inference(avatar_contradiction_clause,[],[f526])).
% 0.18/0.48 cnf(s2, plain, spl7_3 | ~spl7_4, inference(sat_conversion,[],[f108])).
% 0.18/0.48 cnf(s3, plain, spl7_5 | ~spl7_6, inference(sat_conversion,[],[f179])).
% 0.18/0.48 cnf(s5, plain, spl7_4, inference(sat_conversion,[],[f189])).
% 0.18/0.48 cnf(s8, plain, spl7_7 | spl7_10, inference(sat_conversion,[],[f230])).
% 0.18/0.48 cnf(s14, plain, ~spl7_7, inference(sat_conversion,[],[f290])).
% 0.18/0.48 cnf(s15, plain, spl7_6 | ~spl7_10, inference(sat_conversion,[],[f524])).
% 0.18/0.48 cnf(s16, plain, ~spl7_3 | ~spl7_5, inference(sat_conversion,[],[f527])).
% 0.18/0.48 cnf(s19, plain, spl7_10, inference(rat,[],[s8,s14])).
% 0.18/0.48 cnf(s21, plain, spl7_6, inference(rat,[],[s15,s19])).
% 0.18/0.48 cnf(s24, plain, spl7_5, inference(rat,[],[s3,s21])).
% 0.18/0.48 cnf(s25, plain, ~spl7_3, inference(rat,[],[s16,s24])).
% 0.18/0.48 cnf(s26, plain, $false, inference(rat,[],[s2,s5,s25])).
% 0.18/0.48 tff(f540,plain,(
% 0.18/0.48 $false),
% 0.18/0.48 inference(avatar_sat_refutation,[],[s26])).
% 0.18/0.48 % SZS output end Proof for theBenchmark
% 0.18/0.48 % (3284336)------------------------------
% 0.18/0.48 % (3284336)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3284336)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3284336)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3284336)Termination reason: Refutation
% 0.18/0.48 % (3284336)Time elapsed: 0.007 s
% 0.18/0.48 % (3284336)Peak memory usage: 12 MB
% 0.18/0.48 % (3284336)Instructions burned: 19 (million)
% 0.18/0.48 % (3284322)Success in time 0.042 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------