%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP013^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Wed Sep 30 08:07:45 AM UTC 2026
% Result : Theorem 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP013^3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n010.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 19:27:48 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.31 % (3292672)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (3292681)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3013777353:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (3292683)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (3292683)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.22/0.31 % (3292680)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=548210006:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.22/0.31 % (3292678)lrs+10_16_si=on:nwc=1.5:random_seed=1009756282:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (3292679)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1802485777:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (3292681)Instruction limit reached!
% 0.22/0.31 % (3292681)------------------------------
% 0.22/0.31 % (3292681)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3292681)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3292681)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3292681)Termination reason: Instruction limit
% 0.22/0.31 % (3292681)Termination phase: Saturation
% 0.22/0.31 % (3292683)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=3399362174:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (3292681)Time elapsed: 0.009 s
% 0.22/0.31 % (3292681)Peak memory usage: 12 MB
% 0.22/0.31 % (3292681)Instructions burned: 27 (million)
% 0.22/0.31 % (3292679)Instruction limit reached!
% 0.22/0.31 % (3292679)------------------------------
% 0.22/0.31 % (3292679)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3292679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3292679)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3292679)Termination reason: Instruction limit
% 0.22/0.31 % (3292679)Termination phase: Function definition elimination
% 0.22/0.31 % (3292679)Time elapsed: 0.002 s
% 0.22/0.31 % (3292679)Peak memory usage: 10 MB
% 0.22/0.31 % (3292679)Instructions burned: 3 (million)
% 0.22/0.31 % (3292677)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=403034590:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (3292678)Instruction limit reached!
% 0.22/0.31 % (3292678)------------------------------
% 0.22/0.31 % (3292678)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3292678)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3292678)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3292678)Termination reason: Instruction limit
% 0.22/0.31 % (3292678)Termination phase: Saturation
% 0.22/0.31 % (3292678)Time elapsed: 0.012 s
% 0.22/0.31 % (3292678)Peak memory usage: 12 MB
% 0.22/0.31 % (3292678)Instructions burned: 18 (million)
% 0.22/0.31 % (3292680) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3292672-3292680"...
% 0.22/0.31 % (3292682)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1660169389:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (3292689)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1298145532:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (3292689)Instruction limit reached!
% 0.22/0.31 % (3292689)------------------------------
% 0.22/0.31 % (3292689)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3292689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3292689)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3292689)Termination reason: Instruction limit
% 0.22/0.31 % (3292689)Termination phase: Function definition elimination
% 0.22/0.31 % (3292689)Time elapsed: 0.001 s
% 0.22/0.31 % (3292689)Peak memory usage: 10 MB
% 0.22/0.31 % (3292689)Instructions burned: 3 (million)
% 0.22/0.31 % (3292680)...printing done.
% 0.22/0.31 % (3292680)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% 0.22/0.31 thf(type_def_5, type, tyop_2Efcp_2Ecart: ($tType * $tType) > $tType).
% 0.22/0.31 thf(type_def_6, type, tyop_2Emin_2Ebool: $tType).
% 0.22/0.31 thf(type_def_7, type, tyop_2Emin_2Efun: ($tType * $tType) > $tType).
% 0.22/0.31 thf(type_def_8, type, tyop_2Enum_2Enum: $tType).
% 0.22/0.31 thf(type_def_9, type, sTfun: ($tType * $tType) > $tType).
% 0.22/0.31 thf(type_def_10, type, sK1: $tType).
% 0.22/0.31 thf(func_def_0, type, c_2Ebool_2E_21: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.31 thf(func_def_1, type, c_2Earithmetic_2E_2B: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum)).
% 0.22/0.31 thf(func_def_2, type, c_2Earithmetic_2E_2D: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > tyop_2Enum_2Enum)).
% 0.22/0.31 thf(func_def_3, type, c_2Ebool_2E_2F_5C: ($o > $o > $o)).
% 0.22/0.31 thf(func_def_4, type, c_2Earithmetic_2E_3C_3D: (tyop_2Enum_2Enum > tyop_2Enum_2Enum > $o)).
% 0.22/0.31 thf(func_def_5, type, c_2Emin_2E_3D: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.22/0.31 thf(func_def_6, type, c_2Emin_2E_3D_3D_3E: ($o > $o > $o)).
% 0.22/0.31 thf(func_def_7, type, c_2Ebool_2E_3F: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.22/0.31 thf(func_def_8, type, c_2Ebool_2ECOND: !>[X0: $tType]:(($o > X0 > X0 > X0))).
% 0.22/0.31 thf(func_def_9, type, c_2Ebool_2EF: $o).
% 0.22/0.31 thf(func_def_10, type, c_2Ebool_2ET: $o).
% 0.22/0.31 thf(func_def_11, type, c_2Ebool_2E_5C_2F: ($o > $o > $o)).
% 0.22/0.31 thf(func_def_12, type, c_2Ewords_2En2w: !>[X0: $tType]:((tyop_2Enum_2Enum > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.22/0.31 thf(func_def_13, type, c_2Ewords_2Eword__2comp: !>[X0: $tType]:((tyop_2Efcp_2Ecart @ $o @ X0 > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.22/0.31 thf(func_def_14, type, c_2Ewords_2Eword__add: !>[X0: $tType]:((tyop_2Efcp_2Ecart @ $o @ X0 > tyop_2Efcp_2Ecart @ $o @ X0 > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.22/0.31 thf(func_def_15, type, c_2Ewords_2Eword__sub: !>[X0: $tType]:((tyop_2Efcp_2Ecart @ $o @ X0 > tyop_2Efcp_2Ecart @ $o @ X0 > tyop_2Efcp_2Ecart @ $o @ X0))).
% 0.22/0.31 thf(func_def_16, type, c_2Ebool_2E_7E: ($o > $o)).
% 0.22/0.31 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.22/0.31 thf(func_def_21, type, sK0: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.31 thf(func_def_22, type, sK2: tyop_2Enum_2Enum).
% 0.22/0.31 thf(func_def_23, type, sK3: tyop_2Enum_2Enum).
% 0.22/0.31 thf(func_def_24, type, sK4: !>[X0: $tType]:(((X0 > $o) > X0))).
% 0.22/0.31 thf(f10,axiom,(
% 0.22/0.31 ! [X0 : $tType,X1 : X0] : (c_2Ebool_2ET <=> (X1 = X1))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2EREFL__CLAUSE)).
% 0.22/0.31 thf(f16,axiom,(
% 0.22/0.31 ! [X0 : $tType] : (! [X3 : X0,X4 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X3 @ X4)) = X4) & ! [X1 : X0,X2 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X1 @ X2)) = X1))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ebool_2Ebool__case__thm)).
% 0.22/0.31 thf(f17,axiom,(
% 0.22/0.31 ! [X0 : $tType,X2 : tyop_2Efcp_2Ecart @ $o @ X0,X1 : tyop_2Efcp_2Ecart @ $o @ X0] : (((c_2Ewords_2Eword__sub @ X0 @ X1 @ X2)) = ((c_2Ewords_2Eword__add @ X0 @ X1 @ (c_2Ewords_2Eword__2comp @ X0 @ X2))))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2Eword__sub__def)).
% 0.22/0.31 thf(f18,axiom,(
% 0.22/0.31 ! [X1 : $tType,X0 : $tType] : (! [X5 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum] : (((c_2Ewords_2Eword__add @ X1 @ (c_2Ewords_2En2w @ X1 @ X4) @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ X5)))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X1 @ (c_2Earithmetic_2E_3C_3D @ X5 @ X4) @ (c_2Ewords_2En2w @ X1 @ (c_2Earithmetic_2E_2D @ X4 @ X5)) @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ (c_2Earithmetic_2E_2D @ X5 @ X4)))))) & ! [X3 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((c_2Ewords_2Eword__add @ X0 @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ X2)) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ X3)))) = ((c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2B @ X2 @ X3))))))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2EWORD__LITERAL__ADD)).
% 0.22/0.31 thf(f19,conjecture,(
% 0.22/0.31 ! [X0 : $tType,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2E_3C_3D @ X2 @ X1) => (((c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X1 @ X2))) = ((c_2Ewords_2Eword__sub @ X0 @ (c_2Ewords_2En2w @ X0 @ X1) @ (c_2Ewords_2En2w @ X0 @ X2)))))),
% 0.22/0.31 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm_2Ewords_2En2w__sub)).
% 0.22/0.31 thf(f20,negated_conjecture,(
% 0.22/0.31 ~ ! [X0 : $tType,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2E_3C_3D @ X2 @ X1) => (((c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X1 @ X2))) = ((c_2Ewords_2Eword__sub @ X0 @ (c_2Ewords_2En2w @ X0 @ X1) @ (c_2Ewords_2En2w @ X0 @ X2)))))),
% 0.22/0.31 inference(negated_conjecture,[status(cth)],[f19])).
% 0.22/0.31 thf(f31,plain,(
% 0.22/0.31 ! [X0 : $tType,X1 : X0] : (c_2Ebool_2ET <=> (X1 = X1))),
% 0.22/0.31 inference(rectify,[],[f10])).
% 0.22/0.31 thf(f32,plain,(
% 0.22/0.31 ! [X0 : $tType,X1 : X0] : ((c_2Ebool_2ET = $true) <=> (X1 = X1))),
% 0.22/0.31 inference(fool_elimination,[],[f31])).
% 0.22/0.31 thf(f49,plain,(
% 0.22/0.31 ~ ! [X0 : $tType,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((c_2Earithmetic_2E_3C_3D @ X1 @ X2) => (((c_2Ewords_2Eword__sub @ X0 @ (c_2Ewords_2En2w @ X0 @ X2) @ (c_2Ewords_2En2w @ X0 @ X1))) = ((c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X2 @ X1)))))),
% 0.22/0.31 inference(rectify,[],[f20])).
% 0.22/0.31 thf(f50,plain,(
% 0.22/0.31 ~ ! [X0 : $tType,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (($true = ((c_2Earithmetic_2E_3C_3D @ X1 @ X2))) => (((c_2Ewords_2Eword__sub @ X0 @ (c_2Ewords_2En2w @ X0 @ X2) @ (c_2Ewords_2En2w @ X0 @ X1))) = ((c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X2 @ X1)))))),
% 0.22/0.31 inference(fool_elimination,[],[f49])).
% 0.22/0.31 thf(f51,plain,(
% 0.22/0.31 ! [X1 : $tType,X0 : $tType] : (! [X3 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : (((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ (c_2Earithmetic_2E_3C_3D @ X2 @ X3) @ (c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X3 @ X2)) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X2 @ X3))))) = ((c_2Ewords_2Eword__add @ X0 @ (c_2Ewords_2En2w @ X0 @ X3) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ X2))))) & ! [X5 : tyop_2Enum_2Enum,X4 : tyop_2Enum_2Enum] : (((c_2Ewords_2Eword__add @ X1 @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ X5)) @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ X4)))) = ((c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ (c_2Earithmetic_2E_2B @ X5 @ X4))))))),
% 0.22/0.31 inference(rectify,[],[f18])).
% 0.22/0.31 thf(f53,plain,(
% 0.22/0.31 ! [X0 : $tType] : (! [X4 : X0,X3 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X3 @ X4)) = X3) & ! [X1 : X0,X2 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X1 @ X2)) = X2))),
% 0.22/0.31 inference(rectify,[],[f16])).
% 0.22/0.31 thf(f58,plain,(
% 0.22/0.31 ? [X0 : $tType,X2 : tyop_2Enum_2Enum,X1 : tyop_2Enum_2Enum] : ((((c_2Ewords_2Eword__sub @ X0 @ (c_2Ewords_2En2w @ X0 @ X2) @ (c_2Ewords_2En2w @ X0 @ X1))) != ((c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X2 @ X1)))) & ($true = ((c_2Earithmetic_2E_3C_3D @ X1 @ X2))))),
% 0.22/0.31 inference(ennf_transformation,[],[f50])).
% 0.22/0.31 thf(f66,plain,(
% 0.22/0.31 ! [X0 : $tType,X1 : tyop_2Efcp_2Ecart @ $o @ X0,X2 : tyop_2Efcp_2Ecart @ $o @ X0] : (((c_2Ewords_2Eword__sub @ X0 @ X2 @ X1)) = ((c_2Ewords_2Eword__add @ X0 @ X2 @ (c_2Ewords_2Eword__2comp @ X0 @ X1))))),
% 0.22/0.31 inference(rectify,[],[f17])).
% 0.22/0.31 thf(f67,plain,(
% 0.22/0.31 ! [X0 : $tType,X1 : X0] : (((c_2Ebool_2ET = $true) | (X1 != X1)) & ((X1 = X1) | (c_2Ebool_2ET != $true)))),
% 0.22/0.31 inference(nnf_transformation,[],[f32])).
% 0.22/0.31 thf(f87,plain,(
% 0.22/0.31 ! [X0 : $tType,X1 : $tType] : (! [X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : (((c_2Ewords_2Eword__add @ X1 @ (c_2Ewords_2En2w @ X1 @ X2) @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ X3)))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X1 @ (c_2Earithmetic_2E_3C_3D @ X3 @ X2) @ (c_2Ewords_2En2w @ X1 @ (c_2Earithmetic_2E_2D @ X2 @ X3)) @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ (c_2Earithmetic_2E_2D @ X3 @ X2)))))) & ! [X4 : tyop_2Enum_2Enum,X5 : tyop_2Enum_2Enum] : (((c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2B @ X4 @ X5)))) = ((c_2Ewords_2Eword__add @ X0 @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ X4)) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ X5))))))),
% 0.22/0.31 inference(rectify,[],[f51])).
% 0.22/0.31 thf(f88,plain,(
% 0.22/0.31 ! [X0 : $tType] : (! [X1 : X0,X2 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X2 @ X1)) = X2) & ! [X3 : X0,X4 : X0] : (((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2EF @ X3 @ X4)) = X4))),
% 0.22/0.31 inference(rectify,[],[f53])).
% 0.22/0.31 thf(f92,plain,(
% 0.22/0.31 ? [X0 : $tType,X1 : tyop_2Enum_2Enum,X2 : tyop_2Enum_2Enum] : ((((c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ X1 @ X2))) != ((c_2Ewords_2Eword__sub @ X0 @ (c_2Ewords_2En2w @ X0 @ X1) @ (c_2Ewords_2En2w @ X0 @ X2)))) & (((c_2Earithmetic_2E_3C_3D @ X2 @ X1)) = $true))),
% 0.22/0.31 inference(rectify,[],[f58])).
% 0.22/0.31 thf(f93,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK1 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) != ((c_2Ewords_2Eword__sub @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK2) @ (c_2Ewords_2En2w @ sK1 @ sK3)))) & (((c_2Earithmetic_2E_3C_3D @ sK3 @ sK2)) = $true)),
% 0.22/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f92])).
% 0.22/0.31 thf(f104,plain,(
% 0.22/0.31 ( ! [X0 : $tType,X2 : tyop_2Efcp_2Ecart @ $o @ X0,X1 : tyop_2Efcp_2Ecart @ $o @ X0] : ((((c_2Ewords_2Eword__sub @ X0 @ X2 @ X1)) = ((c_2Ewords_2Eword__add @ X0 @ X2 @ (c_2Ewords_2Eword__2comp @ X0 @ X1))))) )),
% 0.22/0.31 inference(cnf_transformation,[],[f66])).
% 0.22/0.31 thf(f106,plain,(
% 0.22/0.31 ( ! [X1 : X0] : ((c_2Ebool_2ET = $true) | (X1 != X1)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f67])).
% 0.22/0.31 thf(f164,plain,(
% 0.22/0.31 ( ! [X1 : $tType,X2 : tyop_2Enum_2Enum,X3 : tyop_2Enum_2Enum] : ((((c_2Ewords_2Eword__add @ X1 @ (c_2Ewords_2En2w @ X1 @ X2) @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ X3)))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X1 @ (c_2Earithmetic_2E_3C_3D @ X3 @ X2) @ (c_2Ewords_2En2w @ X1 @ (c_2Earithmetic_2E_2D @ X2 @ X3)) @ (c_2Ewords_2Eword__2comp @ X1 @ (c_2Ewords_2En2w @ X1 @ (c_2Earithmetic_2E_2D @ X3 @ X2))))))) )),
% 0.22/0.31 inference(cnf_transformation,[],[f87])).
% 0.22/0.31 thf(f166,plain,(
% 0.22/0.31 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ c_2Ebool_2ET @ X2 @ X1)) = X2)) )),
% 0.22/0.31 inference(cnf_transformation,[],[f88])).
% 0.22/0.31 thf(f170,plain,(
% 0.22/0.31 (((c_2Earithmetic_2E_3C_3D @ sK3 @ sK2)) = $true)),
% 0.22/0.31 inference(cnf_transformation,[],[f93])).
% 0.22/0.31 thf(f171,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK1 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) != ((c_2Ewords_2Eword__sub @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK2) @ (c_2Ewords_2En2w @ sK1 @ sK3))))),
% 0.22/0.31 inference(cnf_transformation,[],[f93])).
% 0.22/0.31 thf(f255,plain,(
% 0.22/0.31 (c_2Ebool_2ET = $true)),
% 0.22/0.31 inference(trivial_inequality_removal,[],[f106])).
% 0.22/0.31 thf(f276,definition,(
% 0.22/0.31 spl5_1 <=> (c_2Ebool_2ET = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.22/0.31 thf(f278,plain,(
% 0.22/0.31 (c_2Ebool_2ET = $true) | ~spl5_1),
% 0.22/0.31 inference(avatar_component_clause,[],[f276])).
% 0.22/0.31 thf(f289,definition,(
% 0.22/0.31 spl5_4 <=> (((c_2Earithmetic_2E_3C_3D @ sK3 @ sK2)) = $true)),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition])).
% 0.22/0.31 thf(f291,plain,(
% 0.22/0.31 (((c_2Earithmetic_2E_3C_3D @ sK3 @ sK2)) = $true) | ~spl5_4),
% 0.22/0.31 inference(avatar_component_clause,[],[f289])).
% 0.22/0.31 thf(f292,plain,(
% 0.22/0.31 spl5_4),
% 0.22/0.31 inference(avatar_split_clause,[],[f170,f289])).
% 0.22/0.31 thf(f296,plain,(
% 0.22/0.31 spl5_1),
% 0.22/0.31 inference(avatar_split_clause,[],[f255,f276])).
% 0.22/0.31 thf(f311,definition,(
% 0.22/0.31 spl5_7 <=> (((c_2Ewords_2En2w @ sK1 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) = ((c_2Ewords_2Eword__sub @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK2) @ (c_2Ewords_2En2w @ sK1 @ sK3))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition])).
% 0.22/0.31 thf(f313,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK1 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) != ((c_2Ewords_2Eword__sub @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK2) @ (c_2Ewords_2En2w @ sK1 @ sK3)))) | spl5_7),
% 0.22/0.31 inference(avatar_component_clause,[],[f311])).
% 0.22/0.31 thf(f314,plain,(
% 0.22/0.31 ~spl5_7),
% 0.22/0.31 inference(avatar_split_clause,[],[f171,f311])).
% 0.22/0.31 thf(f328,plain,(
% 0.22/0.31 ( ! [X0 : $tType,X2 : X0,X1 : X0] : ((((c_2Ebool_2ECOND @ X0 @ $true @ X2 @ X1)) = X2)) ) | ~spl5_1),
% 0.22/0.31 inference(forward_demodulation,[],[f166,f278])).
% 0.22/0.31 thf(f373,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK1 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) != ((c_2Ewords_2Eword__add @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK2) @ (c_2Ewords_2Eword__2comp @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK3))))) | spl5_7),
% 0.22/0.31 inference(superposition,[],[f313,f104])).
% 0.22/0.31 thf(f375,definition,(
% 0.22/0.31 spl5_9 <=> (((c_2Ewords_2En2w @ sK1 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) = ((c_2Ewords_2Eword__add @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK2) @ (c_2Ewords_2Eword__2comp @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK3)))))),
% 0.22/0.31 introduced(definition,[new_symbols(definition,[spl5_9])],[avatar_definition])).
% 0.22/0.31 thf(f377,plain,(
% 0.22/0.31 (((c_2Ewords_2En2w @ sK1 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) != ((c_2Ewords_2Eword__add @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK2) @ (c_2Ewords_2Eword__2comp @ sK1 @ (c_2Ewords_2En2w @ sK1 @ sK3))))) | spl5_9),
% 0.22/0.31 inference(avatar_component_clause,[],[f375])).
% 0.22/0.31 thf(f378,plain,(
% 0.22/0.31 ~spl5_9 | spl5_7),
% 0.22/0.31 inference(avatar_split_clause,[],[f373,f311,f375])).
% 0.22/0.31 thf(f383,plain,(
% 0.22/0.31 ( ! [X0 : $tType] : ((((c_2Ewords_2Eword__add @ X0 @ (c_2Ewords_2En2w @ X0 @ sK2) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ sK3)))) = ((c_2Ebool_2ECOND @ tyop_2Efcp_2Ecart @ $o @ X0 @ $true @ (c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3)) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ sK3 @ sK2))))))) ) | ~spl5_4),
% 0.22/0.31 inference(superposition,[],[f164,f291])).
% 0.22/0.31 thf(f392,plain,(
% 0.22/0.31 ( ! [X0 : $tType] : ((((c_2Ewords_2En2w @ X0 @ (c_2Earithmetic_2E_2D @ sK2 @ sK3))) = ((c_2Ewords_2Eword__add @ X0 @ (c_2Ewords_2En2w @ X0 @ sK2) @ (c_2Ewords_2Eword__2comp @ X0 @ (c_2Ewords_2En2w @ X0 @ sK3)))))) ) | (~spl5_1 | ~spl5_4)),
% 0.22/0.31 inference(forward_demodulation,[],[f383,f328])).
% 0.22/0.31 thf(f398,plain,(
% 0.22/0.31 $false | (~spl5_1 | ~spl5_4 | spl5_9)),
% 0.22/0.31 inference(forward_subsumption_resolution,[],[f377,f392])).
% 0.22/0.31 thf(f399,plain,(
% 0.22/0.31 ~spl5_1 | ~spl5_4 | spl5_9),
% 0.22/0.31 inference(avatar_contradiction_clause,[],[f398])).
% 0.22/0.31 cnf(s3, plain, spl5_4, inference(sat_conversion,[],[f292])).
% 0.22/0.31 cnf(s7, plain, spl5_1, inference(sat_conversion,[],[f296])).
% 0.22/0.31 cnf(s20, plain, ~spl5_7, inference(sat_conversion,[],[f314])).
% 0.22/0.31 cnf(s23, plain, spl5_7 | ~spl5_9, inference(sat_conversion,[],[f378])).
% 0.22/0.31 cnf(s24, plain, ~spl5_1 | ~spl5_4 | spl5_9, inference(sat_conversion,[],[f399])).
% 0.22/0.31 cnf(s25, plain, ~spl5_9, inference(rat,[],[s23,s20])).
% 0.22/0.31 cnf(s26, plain, ~spl5_4, inference(rat,[],[s24,s25,s7])).
% 0.22/0.31 cnf(s28, plain, $false, inference(rat,[],[s3,s26])).
% 0.22/0.31 thf(f400,plain,(
% 0.22/0.31 $false),
% 0.22/0.31 inference(avatar_sat_refutation,[],[s28])).
% 0.22/0.31 % SZS output end Proof for theBenchmark
% 0.22/0.31 % (3292680)------------------------------
% 0.22/0.31 % (3292680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (3292680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (3292680)CaDiCaL version: 2.1.3
% 0.22/0.31 % (3292680)Termination reason: Refutation
% 0.22/0.31 % (3292680)Time elapsed: 0.014 s
% 0.22/0.31 % (3292680)Peak memory usage: 13 MB
% 0.22/0.31 % (3292680)Instructions burned: 22 (million)
% 0.22/0.31 % (3292672)Success in time 0.059 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------