%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ANA102^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 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 07:46:04 AM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA102^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.17 % Computer : n015.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:44:48 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.19/0.26 % (3872198)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (3872206)dis+10_1_sil=32000:sp=arity:random_seed=2239267240:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (3872204)% WARNING: option uhcvi not known.
% 0.19/0.26 % (3872206) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3872198-3872206"...
% 0.19/0.26 % (3872203)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=981828079_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26 % (3872204)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3375095758:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26 % (3872205)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3616548369:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.26 % (3872207)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2372096476:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26 % (3872204)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % (3872206)...printing done.
% 0.19/0.26 % (3872207)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.26 % Exception at run slice level
% 0.19/0.26 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.26 % (3872204)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.26 % (3872206)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% 0.19/0.26 thf(type_def_5, type, 'type/realax/real': $tType).
% 0.19/0.26 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.19/0.26 thf(type_def_7, type, sK0: $tType).
% 0.19/0.26 thf(func_def_0, type, 'const/sets/UNION': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0 > $o))).
% 0.19/0.26 thf(func_def_1, type, 'const/sets/SUBSET': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.19/0.26 thf(func_def_2, type, 'const/sets/INTER': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0 > $o))).
% 0.19/0.26 thf(func_def_3, type, 'const/sets/FINITE': !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.19/0.26 thf(func_def_4, type, 'const/sets/EMPTY': !>[X0: $tType]:((X0 > $o))).
% 0.19/0.26 thf(func_def_5, type, 'const/sets/DISJOINT': !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > $o))).
% 0.19/0.26 thf(func_def_6, type, 'const/realax/real_add': ('type/realax/real' > 'type/realax/real' > 'type/realax/real')).
% 0.19/0.26 thf(func_def_7, type, 'const/iterate/sum': !>[X0: $tType]:(((X0 > $o) > (X0 > 'type/realax/real') > 'type/realax/real'))).
% 0.19/0.26 thf(func_def_11, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.19/0.26 thf(func_def_12, type, sK1: (sK0 > 'type/realax/real')).
% 0.19/0.26 thf(func_def_13, type, sK2: (sK0 > $o)).
% 0.19/0.26 thf(func_def_14, type, sK3: (sK0 > $o)).
% 0.19/0.26 thf(func_def_15, type, sK4: (sK0 > $o)).
% 0.19/0.26 thf(func_def_16, type, vNOT: ($o > $o)).
% 0.19/0.26 thf(func_def_17, type, sK5: !>[X0: $tType]:(((X0 > $o) > (X0 > $o) > X0))).
% 0.19/0.26 thf(f1,axiom,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_1')).
% 0.19/0.26 thf(f2,axiom,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/SUBSET_UNION_0')).
% 0.19/0.26 thf(f3,axiom,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/FINITE_SUBSET_')).
% 0.19/0.26 thf(f4,axiom,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/DISJOINT' @ X0 @ X1 @ X2)) = ((('const/sets/INTER' @ X0 @ X1 @ X2)) = 'const/sets/EMPTY' @ X0))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/sets/DISJOINT_')).
% 0.19/0.26 thf(f5,axiom,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o)] : ((('const/sets/DISJOINT' @ X0 @ X2 @ X3) & ('const/sets/FINITE' @ X0 @ X3) & ('const/sets/FINITE' @ X0 @ X2)) => ((('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)))))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_')).
% 0.19/0.26 thf(f6,conjecture,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o),X4 : (X0 > $o)] : ((((('const/sets/UNION' @ X0 @ X2 @ X3)) = X4) & ((('const/sets/INTER' @ X0 @ X2 @ X3)) = 'const/sets/EMPTY' @ X0) & ('const/sets/FINITE' @ X0 @ X4)) => ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) = (('const/iterate/sum' @ X0 @ X4 @ X1))))),
% 0.19/0.26 file('/export/starexec/sandbox/benchmark/theBenchmark.p','thm/iterate/SUM_UNION_EQ_')).
% 0.19/0.26 thf(f7,negated_conjecture,(
% 0.19/0.26 ~ ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o),X4 : (X0 > $o)] : ((((('const/sets/UNION' @ X0 @ X2 @ X3)) = X4) & ((('const/sets/INTER' @ X0 @ X2 @ X3)) = 'const/sets/EMPTY' @ X0) & ('const/sets/FINITE' @ X0 @ X4)) => ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) = (('const/iterate/sum' @ X0 @ X4 @ X1))))),
% 0.19/0.26 inference(negated_conjecture,[status(cth)],[f6])).
% 0.19/0.26 thf(f8,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1))),
% 0.19/0.26 inference(rectify,[],[f1])).
% 0.19/0.26 thf(f9,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1))) = $true)),
% 0.19/0.26 inference(fool_elimination,[],[f8])).
% 0.19/0.26 thf(f10,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2))),
% 0.19/0.26 inference(rectify,[],[f2])).
% 0.19/0.26 thf(f11,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2))) = $true)),
% 0.19/0.26 inference(fool_elimination,[],[f10])).
% 0.19/0.26 thf(f12,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) & ('const/sets/FINITE' @ X0 @ X2)) => ('const/sets/FINITE' @ X0 @ X1))),
% 0.19/0.26 inference(rectify,[],[f3])).
% 0.19/0.26 thf(f13,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ((('const/sets/FINITE' @ X0 @ X1)) = $true))),
% 0.19/0.26 inference(fool_elimination,[],[f12])).
% 0.19/0.26 thf(f14,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : ((('const/sets/DISJOINT' @ X0 @ X1 @ X2)) = ((('const/sets/INTER' @ X0 @ X1 @ X2) = 'const/sets/EMPTY' @ X0)))),
% 0.19/0.26 inference(fool_elimination,[],[f4])).
% 0.19/0.26 thf(f15,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o)] : ((('const/sets/DISJOINT' @ X0 @ X2 @ X3) & ('const/sets/FINITE' @ X0 @ X3) & ('const/sets/FINITE' @ X0 @ X2)) => ((('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)))))),
% 0.19/0.26 inference(rectify,[],[f5])).
% 0.19/0.26 thf(f16,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o)] : ((((('const/sets/DISJOINT' @ X0 @ X2 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X3)) = $true) & ((('const/sets/FINITE' @ X0 @ X2)) = $true)) => ((('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)))))),
% 0.19/0.26 inference(fool_elimination,[],[f15])).
% 0.19/0.26 thf(f17,plain,(
% 0.19/0.26 ~ ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o),X4 : (X0 > $o)] : ((((('const/sets/UNION' @ X0 @ X2 @ X3)) = X4) & ((('const/sets/INTER' @ X0 @ X2 @ X3)) = 'const/sets/EMPTY' @ X0) & ('const/sets/FINITE' @ X0 @ X4)) => ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) = (('const/iterate/sum' @ X0 @ X4 @ X1))))),
% 0.19/0.26 inference(rectify,[],[f7])).
% 0.19/0.26 thf(f18,plain,(
% 0.19/0.26 ~ ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o),X4 : (X0 > $o)] : ((((('const/sets/UNION' @ X0 @ X2 @ X3)) = X4) & ('const/sets/EMPTY' @ X0 = (('const/sets/INTER' @ X0 @ X2 @ X3))) & ((('const/sets/FINITE' @ X0 @ X4)) = $true)) => ((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) = (('const/iterate/sum' @ X0 @ X4 @ X1))))),
% 0.19/0.26 inference(fool_elimination,[],[f17])).
% 0.19/0.26 thf(f19,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) | (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)))),
% 0.19/0.26 inference(ennf_transformation,[],[f13])).
% 0.19/0.26 thf(f20,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > $o),X2 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 0.19/0.26 inference(flattening,[],[f19])).
% 0.19/0.26 thf(f21,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o)] : (((('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)))) | (((('const/sets/DISJOINT' @ X0 @ X2 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)))),
% 0.19/0.26 inference(ennf_transformation,[],[f16])).
% 0.19/0.26 thf(f22,plain,(
% 0.19/0.26 ! [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o)] : (((('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)))) | ((('const/sets/DISJOINT' @ X0 @ X2 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true))),
% 0.19/0.26 inference(flattening,[],[f21])).
% 0.19/0.26 thf(f23,plain,(
% 0.19/0.26 ? [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o),X4 : (X0 > $o)] : (((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) != (('const/iterate/sum' @ X0 @ X4 @ X1))) & (((('const/sets/UNION' @ X0 @ X2 @ X3)) = X4) & ('const/sets/EMPTY' @ X0 = (('const/sets/INTER' @ X0 @ X2 @ X3))) & ((('const/sets/FINITE' @ X0 @ X4)) = $true)))),
% 0.19/0.26 inference(ennf_transformation,[],[f18])).
% 0.19/0.26 thf(f24,plain,(
% 0.19/0.26 ? [X0 : $tType,X1 : (X0 > 'type/realax/real'),X2 : (X0 > $o),X3 : (X0 > $o),X4 : (X0 > $o)] : (((('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1))) != (('const/iterate/sum' @ X0 @ X4 @ X1))) & ((('const/sets/UNION' @ X0 @ X2 @ X3)) = X4) & ('const/sets/EMPTY' @ X0 = (('const/sets/INTER' @ X0 @ X2 @ X3))) & ((('const/sets/FINITE' @ X0 @ X4)) = $true))),
% 0.19/0.26 inference(flattening,[],[f23])).
% 0.19/0.26 thf(f25,plain,(
% 0.19/0.26 ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1))) != (('const/iterate/sum' @ sK0 @ sK4 @ sK1))) & (sK4 = (('const/sets/UNION' @ sK0 @ sK2 @ sK3))) & ('const/sets/EMPTY' @ sK0 = (('const/sets/INTER' @ sK0 @ sK2 @ sK3))) & ($true = (('const/sets/FINITE' @ sK0 @ sK4)))),
% 0.19/0.26 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f24])).
% 0.19/0.26 thf(f26,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X2 @ X1))) = $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f9])).
% 0.19/0.26 thf(f27,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ ('const/sets/UNION' @ X0 @ X1 @ X2))) = $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f11])).
% 0.19/0.26 thf(f28,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/SUBSET' @ X0 @ X1 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f20])).
% 0.19/0.26 thf(f29,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/DISJOINT' @ X0 @ X1 @ X2)) = ((('const/sets/INTER' @ X0 @ X1 @ X2) = 'const/sets/EMPTY' @ X0)))) )),
% 0.19/0.26 inference(cnf_transformation,[],[f14])).
% 0.19/0.26 thf(f30,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X3 : (X0 > $o),X1 : (X0 > 'type/realax/real')] : (((('const/sets/DISJOINT' @ X0 @ X2 @ X3)) != $true) | ((('const/iterate/sum' @ X0 @ ('const/sets/UNION' @ X0 @ X2 @ X3) @ X1)) = (('const/realax/real_add' @ ('const/iterate/sum' @ X0 @ X2 @ X1) @ ('const/iterate/sum' @ X0 @ X3 @ X1)))) | ((('const/sets/FINITE' @ X0 @ X3)) != $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true)) )),
% 0.19/0.26 inference(cnf_transformation,[],[f22])).
% 0.19/0.26 thf(f31,plain,(
% 0.19/0.26 ($true = (('const/sets/FINITE' @ sK0 @ sK4)))),
% 0.19/0.26 inference(cnf_transformation,[],[f25])).
% 0.19/0.26 thf(f32,plain,(
% 0.19/0.26 ('const/sets/EMPTY' @ sK0 = (('const/sets/INTER' @ sK0 @ sK2 @ sK3)))),
% 0.19/0.26 inference(cnf_transformation,[],[f25])).
% 0.19/0.26 thf(f33,plain,(
% 0.19/0.26 (sK4 = (('const/sets/UNION' @ sK0 @ sK2 @ sK3)))),
% 0.19/0.26 inference(cnf_transformation,[],[f25])).
% 0.19/0.26 thf(f34,plain,(
% 0.19/0.26 ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1))) != (('const/iterate/sum' @ sK0 @ sK4 @ sK1)))),
% 0.19/0.26 inference(cnf_transformation,[],[f25])).
% 0.19/0.26 thf(f36,definition,(
% 0.19/0.26 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.19/0.26 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.19/0.26 thf(f37,plain,(
% 0.19/0.26 ((('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ sK1) @ ('const/iterate/sum' @ sK0 @ sK3 @ sK1))) != (('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ sK1)))),
% 0.19/0.26 inference(definition_unfolding,[],[f34,f33])).
% 0.19/0.26 thf(f38,plain,(
% 0.19/0.26 ($true = (('const/sets/FINITE' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3))))),
% 0.19/0.26 inference(definition_unfolding,[],[f31,f33])).
% 0.19/0.26 thf(f39,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/DISJOINT' @ X0 @ X1 @ X2)) = $true) | (((('const/sets/INTER' @ X0 @ X1 @ X2) = 'const/sets/EMPTY' @ X0)) = $false)) )),
% 0.19/0.26 inference(iff_proxy_clausification,[],[f29])).
% 0.19/0.26 thf(f42,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/INTER' @ X0 @ X1 @ X2)) != 'const/sets/EMPTY' @ X0) | ((('const/sets/DISJOINT' @ X0 @ X1 @ X2)) = $true)) )),
% 0.19/0.26 inference(equality_proxy_clausification,[],[f39])).
% 0.19/0.26 thf(f59,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (($true != $true) | ((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $false)) )),
% 0.19/0.26 inference(constrained_superposition,[],[f28,f36])).
% 0.19/0.26 thf(f60,plain,(
% 0.19/0.26 ( ! [X0 : $tType,X2 : (X0 > $o),X1 : (X0 > $o)] : (((('const/sets/FINITE' @ X0 @ X2)) != $true) | ((('const/sets/FINITE' @ X0 @ X1)) = $true) | ((('const/sets/SUBSET' @ X0 @ X1 @ X2)) = $false)) )),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f59])).
% 0.19/0.26 thf(f61,plain,(
% 0.19/0.26 ( ! [X0 : (sK0 > $o)] : (($true != $true) | ($true = (('const/sets/FINITE' @ sK0 @ X0))) | ($false = (('const/sets/SUBSET' @ sK0 @ X0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3))))) )),
% 0.19/0.26 inference(constrained_superposition,[],[f60,f38])).
% 0.19/0.26 thf(f64,plain,(
% 0.19/0.26 ( ! [X0 : (sK0 > $o)] : (($false = (('const/sets/SUBSET' @ sK0 @ X0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3)))) | ($true = (('const/sets/FINITE' @ sK0 @ X0)))) )),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f61])).
% 0.19/0.26 thf(f70,plain,(
% 0.19/0.26 ($true = $false) | ($true = (('const/sets/FINITE' @ sK0 @ sK3)))),
% 0.19/0.26 inference(constrained_superposition,[],[f26,f64])).
% 0.19/0.26 thf(f71,plain,(
% 0.19/0.26 ($true = (('const/sets/FINITE' @ sK0 @ sK3)))),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f70])).
% 0.19/0.26 thf(f77,plain,(
% 0.19/0.26 ($true = $false) | ($true = (('const/sets/FINITE' @ sK0 @ sK2)))),
% 0.19/0.26 inference(constrained_superposition,[],[f64,f27])).
% 0.19/0.26 thf(f78,plain,(
% 0.19/0.26 ($true = (('const/sets/FINITE' @ sK0 @ sK2)))),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f77])).
% 0.19/0.26 thf(f103,plain,(
% 0.19/0.26 ('const/sets/EMPTY' @ sK0 != 'const/sets/EMPTY' @ sK0) | ($true = (('const/sets/DISJOINT' @ sK0 @ sK2 @ sK3)))),
% 0.19/0.26 inference(constrained_superposition,[],[f42,f32])).
% 0.19/0.26 thf(f106,plain,(
% 0.19/0.26 ($true = (('const/sets/DISJOINT' @ sK0 @ sK2 @ sK3)))),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f103])).
% 0.19/0.26 thf(f109,plain,(
% 0.19/0.26 ( ! [X0 : (sK0 > 'type/realax/real')] : (($true != $true) | ((('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0)) = (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)))) | ($true != (('const/sets/FINITE' @ sK0 @ sK3))) | ($true != (('const/sets/FINITE' @ sK0 @ sK2)))) )),
% 0.19/0.26 inference(constrained_superposition,[],[f30,f106])).
% 0.19/0.26 thf(f110,plain,(
% 0.19/0.26 ( ! [X0 : (sK0 > 'type/realax/real')] : (((('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0)) = (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)))) | ($true != (('const/sets/FINITE' @ sK0 @ sK3))) | ($true != (('const/sets/FINITE' @ sK0 @ sK2)))) )),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f109])).
% 0.19/0.26 thf(f111,plain,(
% 0.19/0.26 ( ! [X0 : (sK0 > 'type/realax/real')] : (((('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0)) = (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0)))) | ($true != (('const/sets/FINITE' @ sK0 @ sK2)))) )),
% 0.19/0.26 inference(forward_subsumption_resolution,[],[f110,f71])).
% 0.19/0.26 thf(f112,plain,(
% 0.19/0.26 ( ! [X0 : (sK0 > 'type/realax/real')] : (((('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ X0)) = (('const/realax/real_add' @ ('const/iterate/sum' @ sK0 @ sK2 @ X0) @ ('const/iterate/sum' @ sK0 @ sK3 @ X0))))) )),
% 0.19/0.26 inference(forward_subsumption_resolution,[],[f111,f78])).
% 0.19/0.26 thf(f188,plain,(
% 0.19/0.26 ((('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ sK1)) != (('const/iterate/sum' @ sK0 @ ('const/sets/UNION' @ sK0 @ sK2 @ sK3) @ sK1)))),
% 0.19/0.26 inference(constrained_superposition,[],[f37,f112])).
% 0.19/0.26 thf(f189,plain,(
% 0.19/0.26 $false),
% 0.19/0.26 inference(trivial_inequality_removal,[],[f188])).
% 0.19/0.26 % SZS output end Proof for theBenchmark
% 0.19/0.26 % (3872206)------------------------------
% 0.19/0.26 % (3872206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.26 % (3872206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.26 % (3872206)CaDiCaL version: 2.1.3
% 0.19/0.26 % (3872206)Termination reason: Refutation
% 0.19/0.26 % (3872206)Time elapsed: 0.007 s
% 0.19/0.26 % (3872206)Peak memory usage: 12 MB
% 0.19/0.26 % (3872206)Instructions burned: 21 (million)
% 0.19/0.26 % (3872198)Success in time 0.046 s
% 0.19/0.26 % Vampire exiting
%------------------------------------------------------------------------------